Landon Noll looking up Fremont Peak Observatory 0.8m telescope Leonid 2001 meteor squall count at Fremont Peak

Curious prime numbers

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It can be argued that every positive integer n has an associated prime curio. The reverse can also be argued. Regardless, there are a number of curious numbers related to primes. We call such numbers ``Prime Curios!''.

Some of the curious numbers below have been submitted and entered into the ``Prime Curios!'' table under the name Noll.

Here are my own set of curious numbers related to primes:

  • 3
    3*23 - 3 - 23 is prime

    3*23 - 3 + 23 is prime

    3*23 + 3 - 23 is prime

  • 4
    4*24 - 4 - 1 is prime

    4*24 - 4 + 1 is prime

    4*24 - 4 - 24 - 1 is prime

    4*24 + 4 - 1 is prime

    4*24 + 4 - 24 + 1 is prime

    4*24 + 4 + 24 - 1 is prime

  • 5
    5*25 + 5 + 25 is prime

  • 6
    6*26 - 1 is prime

    6*26 - 6 + 1 is prime

    6*26 - 6 - 26 - 1 is prime

    6*26 + 6 - 1 is prime

  • 7
    7*27 - 7 - 27 is prime

    7*27 + 7 + 27 is prime

  • 8
    8*28 - 8 - 1 is prime

    8*28 - 8 - 28 - 1 is prime

    8*28 + 8 - 28 + 1 is prime

    8*28 + 8 + 28 - 1 is prime

  • 10
    10*210 + 10 - 210 + 1 is prime

    10*210 + 10 + 210 - 1 is prime

  • 12
    12*212 - 12 - 1 is prime

  • 13
    13*213 + 13 - 213 is prime

  • 16
    16*216 - 16 - 1 is prime

  • 17
    17*217 + 17 - 217 is prime

  • 18
    18*218 - 18 - 218 - 1 is prime

  • 19
    19*219 + 19 - 219 is prime

    19*219 + 19 + 219 is prime

  • 20
    20*220 - 20 - 220 - 1 is prime

  • 21
    21*221 + 21 - 221 is prime

  • 22
    22*222 + 22 - 222 + 1 is prime

  • 27
    27*227 + 27 + 227 is prime

  • 28
    28*228 + 28 + 228 - 1 is prime

  • 30
    30*230 - 1 is prime

    30*230 - 30 + 1 is prime

    30*230 + 30 - 1 is prime

  • 31
    31*231 + 31 + 231 is prime

  • 32
    32*232 - 1 is prime

    32*232 - 32 + 1 is prime

  • 33
    33*233 + 33 + 233 is prime

  • 34
    34*234 + 34 - 1 is prime

  • 37
    37*237 + 37 + 237 is prime

  • 38
    38*238 + 38 + 1 is prime

  • 40
    40*240 - 40 - 1 is prime

  • 42
    42*242 - 42 + 1 is prime

  • 44
    44*244 + 44 + 244 - 1 is prime

  • 45
    45*245 - 45 - 245 is prime

  • 46
    46*246 + 46 + 246 - 1 is prime

  • 48
    48*248 - 48 - 248 - 1 is prime
  • 54
    The sum of the non-prime divisors of 54 is a Mersenne prime exponent.

    The 54th prime is the smallest number that is the sum of three cubes in two ways.

    The sum of denoninators of the Bernoulli numbers less than or equal to 54 is prime.

    1354 + 54 is prime.

  • 56
    Sigma(56) equals the first prime of the form 6n - 1 factorial, 5!

    256 - 1 - 56 + 1 is prime.

    The number of products of distinct primes less than or equal to 11 (the only palindromic prime with an even number of digits) which ar e congruent to -1 mod 11 is 56.

  • 57
    pi(57) = 24 and 5757 - pi(57) is prime.

    57 * 225 - 1 is prime.

    57*257 - 57 + 257 is prime

  • 58
    58*258 + 58 - 258 + 1 is prime

  • 62
    62*262 - 62 - 262 - 1 is prime

  • 64
    64*264 + 64 - 264 + 1 is prime

  • 75
    75*275 - 75 - 275 is prime

  • 76
    76*276 + 76 - 276 + 1 is prime

  • 80
    80*280 - 80 - 1 is prime

  • 81
    81*281 - 81 - 281 is prime

  • 87
    87*287 - 87 - 287 is prime

  • 92
    92*292 - 92 - 292 - 1 is prime

    92*292 + 92 - 292 + 1 is prime

  • 94
    94*294 + 94 - 1 is prime

    94*294 + 94 - 294 + 1 is prime

  • 111
    111 * 2111 - 111 - 2111 is prime.

  • 112
    112*2112 - 112 - 2112 - 1 is prime

    112*2112 + 112 - 2112 + 1 is prime

  • 113
    113*2113 + 113 + 2113 is prime

  • 115
    115*2115 - 115 - 2115 is prime

  • 120
    120*2120 - 120 + 1 is prime

    120*2120 - 120 - 2120 - 1 is prime

  • 122
    122*2122 + 122 - 2122 + 1 is prime

  • 123
    123 * 2123 - 1 is prime.

  • 127
    22127-1-1 has no prime factors less than 5 * 1050.

  • 173
    173*2173 + 173 + 2173 is prime

  • 179
    179*2179 + 179 - 2179 is prime

  • 182
    182*2182 - 182 - 2182 - 1 is prime

  • 210
    210*2210 - 210 + 1 is prime

  • 212
    212*2212 - 212 - 2212 - 1 is prime

  • 216
    216*2216 + 216 - 1 is prime

  • 217
    217*2217 + 217 - 2217 is prime

  • 218
    218*2218 + 218 + 2218 - 1 is prime

  • 225
    225*2225 - 225 - 2225 is prime

  • 232
    232*2232 + 232 + 2232 - 1 is prime

  • 248
    248*2248 - 248 + 1 is prime

  • 256
    256 = (21701 - 19937) - (23209 - 21701). Note the use of three consecutive Mersenne prime exponents!

  • 274
    274*2274 + 274 - 2274 + 1 is prime

  • 284
    284*2284 - 284 + 1 is prime

  • 286
    repeat(286,8) * 2286 - 1 is prime

    repeat(286,22) * 2286 + 286 - 1 is prime

    repeat(286,57) * 2286 + 2286 + 1 is prime

    repeat(286,114) * 2286 - 2286 - 1 is prime

    repeat(286,155) * 2286 + 2286 + 1 is prime

  • 287
    repeat(287,60) * 2287 + 1 is prime

    repeat(287,109) * 2287 + 1 is prime

    repeat(287,110) * 2287 - 2287 - 1 is prime

    repeat(287,118) * 2287 - 2287 - 1 is prime

  • 288
    repeat(288,6) + 1 is prime

    repeat(288,24) + 1 is prime

    repeat(288,34) * 2288 - 1 is prime

    repeat(288,48) * 2288 - 1 is prime

    repeat(288,68) * 2288 + 288 + 1 is prime

    repeat(288,70) + 1 is prime

    repeat(288,98) + 1 is prime

    repeat(288,149) * 2288 - 288 + 1 is prime

    repeat(288,171) + 1 is prime

  • 290
    repeat(290,1) * 2290 + 2290 - 1 is prime

    repeat(290,6) + 1 is prime

    repeat(290,30) * 2290 - 290 + 1 is prime

    repeat(290,59) * 2290 - 290 - 1 is prime

    repeat(290,68) * 2290 + 290 - 1 is prime

    repeat(290,73) * 2290 - 290 - 1 is prime

    repeat(290,131) * 2290 + 1 is prime

    repeat(290,133) * 2290 - 290 - 1 is prime

    repeat(290,176) * 2290 - 290 - 1 is prime

    repeat(290,180) * 2290 + 1 is prime

  • 294
    repeat(294,1) * 2294 + 2294 + 1 is prime

    repeat(294,7) * 2294 + 1 is prime

    repeat(294,11) * 2294 - 294 - 1 is prime

    repeat(294,55) * 2294 + 1 is prime

    repeat(294,182) * 2294 + 1 is prime

    repeat(294,247) * 2294 + 2294 + 1 is prime

  • 295
    repeat(295,12) * 2295 + 1 is prime

    repeat(295,41) * 2295 - 2295 - 1 is prime

    repeat(295,117) * 2295 - 2295 + 1 is prime

    repeat(295,241) * 2295 - 1 is prime

    repeat(295,264) * 2295 + 2295 - 1 is prime

  • 296
    repeat(296,6) + 1 is prime

    repeat(296,22) * 2296 - 296 + 1 is prime

    repeat(296,32) * 2296 + 296 - 1 is prime

    repeat(296,46) * 2296 - 296 + 1 is prime

    repeat(296,50) * 2296 + 296 - 1 is prime

    repeat(296,79) * 2296 + 296 + 1 is prime

    repeat(296,109) * 2296 + 2296 + 1 is prime

    repeat(296,154) * 2296 + 2296 - 1 is prime

    repeat(296,190) * 2296 - 2296 + 1 is prime

    repeat(296,281) * 2296 + 296 + 1 is prime

  • 297
    repeat(297,57) * 2297 - 1 is prime

    repeat(297,67) * 2297 - 2297 + 1 is prime

  • 298
    repeat(298,3) * 2298 - 298 - 1 is prime

    repeat(298,7) * 2298 + 1 is prime

    repeat(298,208) * 2298 + 1 is prime

    repeat(298,220) * 2298 - 2298 + 1 is prime

  • 300
    repeat(300,2) + 1 is prime

    repeat(300,3) * 2300 - 2300 - 1 is prime

    repeat(300,6) + 1 is prime

    repeat(300,13) * 2300 + 2300 + 1 is prime

    repeat(300,18) * 2300 + 2300 + 1 is prime

    repeat(300,30) + 1 is prime

    repeat(300,33) * 2300 - 300 - 1 is prime

    repeat(300,42) * 2300 - 1 is prime

    repeat(300,46) * 2300 + 1 is prime

    repeat(300,51) * 2300 - 300 - 1 is prime

    repeat(300,92) * 2300 + 2300 + 1 is prime

    repeat(300,128) * 2300 - 1 is prime

    repeat(300,143) * 2300 + 300 + 1 is prime

    repeat(300,235) * 2300 - 300 + 1 is prime

    repeat(300,237) * 2300 + 2300 + 1 is prime

    repeat(300,259) * 2300 - 2300 - 1 is prime

  • 301
    repeat(301,19) * 2301 - 2301 + 1 is prime

    repeat(301,24) * 2301 + 1 is prime

    repeat(301,24) * 2301 + 2301 - 1 is prime

    repeat(301,48) * 2301 + 2301 - 1 is prime

    repeat(301,60) * 2301 + 1 is prime

    repeat(301,60) * 2301 - 2301 + 1 is prime

    repeat(301,82) * 2301 - 1 is prime

    repeat(301,102) * 2301 - 2301 + 1 is prime

    repeat(301,120) * 2301 - 1 is prime

  • 302
    repeat(302,6) * 2302 - 1 is prime

    repeat(302,42) + 1 is prime

    repeat(302,62) + 1 is prime

    repeat(302,98) * 2302 + 2302 - 1 is prime

    repeat(302,128) * 2302 + 2302 - 1 is prime

    repeat(302,131) + 1 is prime

    repeat(302,255) * 2302 - 1 is prime

  • 303
    repeat(303,99) * 2303 - 1 is prime

  • 304
    repeat(304,3) * 2304 - 304 - 1 is prime

    repeat(304,10) * 2304 - 304 + 1 is prime

    repeat(304,29) * 2304 - 304 + 1 is prime

    repeat(304,36) * 2304 - 304 - 1 is prime

    repeat(304,37) * 2304 + 304 - 1 is prime

    repeat(304,54) * 2304 + 304 + 1 is prime

    repeat(304,59) * 2304 + 304 + 1 is prime

    repeat(304,67) * 2304 - 304 - 1 is prime

    repeat(304,73) * 2304 - 2304 - 1 is prime

    repeat(304,75) * 2304 + 304 + 1 is prime

    repeat(304,77) * 2304 - 1 is prime

    repeat(304,91) * 2304 + 304 - 1 is prime

    repeat(304,134) * 2304 - 2304 + 1 is prime

    repeat(304,243) * 2304 - 1 is prime

    repeat(304,290) * 2304 - 2304 + 1 is prime

  • 306
    repeat(306,1) + 1 is prime

    repeat(306,4) + 1 is prime

    repeat(306,5) + 1 is prime

    repeat(306,17) * 2306 + 306 - 1 is prime

    repeat(306,32) + 1 is prime

    repeat(306,46) * 2306 + 306 - 1 is prime

    repeat(306,47) * 2306 - 1 is prime

    repeat(306,77) * 2306 - 2306 - 1 is prime

    repeat(306,90) * 2306 - 306 - 1 is prime

    repeat(306,111) * 2306 - 306 - 1 is prime

    repeat(306,129) + 1 is prime

    repeat(306,149) + 1 is prime

    repeat(306,152) * 2306 + 306 - 1 is prime

    repeat(306,161) * 2306 - 1 is prime

    repeat(306,175) + 1 is prime

    repeat(306,247) * 2306 + 306 - 1 is prime

    repeat(306,285) + 1 is prime

  • 308
    repeat(308,2) + 1 is prime

    repeat(308,9) * 2308 + 1 is prime

    repeat(308,30) * 2308 + 1 is prime

    repeat(308,30) * 2308 - 308 + 1 is prime

    repeat(308,45) * 2308 - 1 is prime

    repeat(308,48) + 1 is prime

    repeat(308,99) * 2308 - 308 + 1 is prime

    repeat(308,104) * 2308 + 2308 - 1 is prime

    repeat(308,117) * 2308 - 308 + 1 is prime

    repeat(308,160) * 2308 + 2308 - 1 is prime

    repeat(308,201) * 2308 - 2308 - 1 is prime

  • 309
    repeat(309,4) * 2309 + 1 is prime

    repeat(309,83) * 2309 - 2309 + 1 is prime

    repeat(309,141) * 2309 + 1 is prime

    repeat(309,178) * 2309 + 1 is prime

  • 310
    repeat(310,1) + 1 is prime

    repeat(310,4) + 1 is prime

    repeat(310,8) * 2310 + 310 - 1 is prime

    repeat(310,16) * 2310 + 310 - 1 is prime

    repeat(310,18) * 2310 + 1 is prime

    repeat(310,28) + 1 is prime

    repeat(310,36) * 2310 + 310 + 1 is prime

    repeat(310,48) * 2310 + 310 + 1 is prime

    repeat(310,57) + 1 is prime

    repeat(310,61) * 2310 - 310 - 1 is prime

    repeat(310,73) + 1 is prime

    repeat(310,104) * 2310 - 310 + 1 is prime

    repeat(310,132) * 2310 + 1 is prime

    repeat(310,141) * 2310 - 310 - 1 is prime

    repeat(310,160) * 2310 + 310 - 1 is prime

    repeat(310,173) * 2310 - 310 + 1 is prime

    repeat(310,182) * 2310 + 310 + 1 is prime

    repeat(310,190) * 2310 + 1 is prime

    repeat(310,295) * 2310 + 1 is prime

  • 312
    repeat(312,1) + 1 is prime

    repeat(312,2) + 1 is prime

    repeat(312,20) * 2312 - 1 is prime

    repeat(312,26) + 1 is prime

    repeat(312,29) + 1 is prime

    repeat(312,51) * 2312 + 1 is prime

    repeat(312,89) + 1 is prime

    repeat(312,108) * 2312 + 1 is prime

    repeat(312,174) * 2312 + 2312 + 1 is prime

    repeat(312,198) * 2312 - 312 + 1 is prime

    repeat(312,223) * 2312 - 312 + 1 is prime

    repeat(312,232) + 1 is prime

    repeat(312,241) + 1 is prime

    repeat(312,259) * 2312 - 312 + 1 is prime

  • 314
    314*2314 - 314 - 1 is prime

  • 315
    repeat(315,15) * 2315 - 1 is prime

    repeat(315,18) * 2315 + 1 is prime

  • 316
    repeat(316,1) + 1 is prime

    repeat(316,7) + 1 is prime

    repeat(316,7) * 2316 + 316 - 1 is prime

    repeat(316,13) + 1 is prime

    repeat(316,130) * 2316 - 2316 + 1 is prime

    repeat(316,286) * 2316 - 2316 + 1 is prime

    repeat(316,290) * 2316 + 2316 + 1 is prime

    repeat(316,301) * 2316 - 2316 + 1 is prime

    repeat(316,309) + 1 is prime

  • 318
    318*2318 - 318 - 2318 - 1 is prime

  • 321
    repeat(321,56) * 2321 + 1 is prime

    repeat(321,85) * 2321 - 2321 + 1 is prime

    repeat(321,117) * 2321 + 2321 - 1 is prime

    repeat(321,205) * 2321 + 2321 - 1 is prime

  • 322
    repeat(322,37) * 2322 + 322 - 1 is prime

    repeat(322,153) * 2322 + 1 is prime

    repeat(322,272) * 2322 + 322 - 1 is prime

    repeat(322,302) * 2322 + 2322 - 1 is prime

    repeat(322,319) * 2322 + 2322 - 1 is prime

  • 325
    repeat(325,1) * 2325 - 2325 - 1 is prime

    repeat(325,96) * 2325 + 2325 - 1 is prime

  • 326
    repeat(326,7) * 2326 - 1 is prime

    repeat(326,16) * 2326 - 326 - 1 is prime

    repeat(326,17) + 1 is prime

    repeat(326,41) + 1 is prime

    repeat(326,43) * 2326 - 326 + 1 is prime

    repeat(326,96) + 1 is prime

    repeat(326,199) * 2326 - 326 + 1 is prime

    repeat(326,231) * 2326 - 2326 - 1 is prime

    repeat(326,243) * 2326 - 326 + 1 is prime

    repeat(326,248) * 2326 - 2326 + 1 is prime

    repeat(326,269) * 2326 - 2326 - 1 is prime

  • 327
    repeat(327,71) * 2327 + 1 is prime

    repeat(327,71) * 2327 + 1 is prime

  • 328
    repeat(328,4) + 1 is prime

    repeat(328,12) + 1 is prime

    repeat(328,14) * 2328 - 328 + 1 is prime

    repeat(328,36) * 2328 + 1 is prime

    repeat(328,40) * 2328 + 1 is prime

    repeat(328,45) * 2328 - 328 - 1 is prime

    repeat(328,56) * 2328 - 2328 + 1 is prime

    repeat(328,59) * 2328 - 1 is prime

    repeat(328,104) * 2328 + 2328 - 1 is prime

    repeat(328,108) * 2328 - 1 is prime

    repeat(328,116) * 2328 + 2328 - 1 is prime

    repeat(328,255) * 2328 + 1 is prime

    repeat(328,324) * 2328 + 1 is prime

    repeat(328,328) * 2328 - 2328 - 1 is prime

  • 329
    repeat(329,13) * 2329 + 1 is prime

    repeat(329,86) * 2329 - 2329 + 1 is prime

    repeat(329,90) * 2329 - 2329 + 1 is prime

    repeat(329,138) * 2329 - 2329 + 1 is prime

    repeat(329,139) * 2329 + 1 is prime

    repeat(329,190) * 2329 + 1 is prime

  • 330
    repeat(330,1) + 1 is prime

    repeat(330,2) + 1 is prime

    repeat(330,4) * 2330 + 1 is prime

    repeat(330,8) + 1 is prime

    repeat(330,12) * 2330 - 330 - 1 is prime

    repeat(330,14) + 1 is prime

    repeat(330,17) + 1 is prime

    repeat(330,18) * 2330 - 330 - 1 is prime

    repeat(330,28) * 2330 - 330 - 1 is prime

    repeat(330,30) * 2330 + 1 is prime

    repeat(330,46) + 1 is prime

    repeat(330,48) * 2330 - 330 - 1 is prime

    repeat(330,110) * 2330 - 1 is prime

    repeat(330,133) * 2330 - 330 + 1 is prime

    repeat(330,140) * 2330 + 1 is prime

    repeat(330,162) * 2330 + 330 + 1 is prime

    repeat(330,179) * 2330 - 330 - 1 is prime

    repeat(330,207) + 1 is prime

  • 332
    repeat(332,3) + 1 is prime

    repeat(332,8) + 1 is prime

    repeat(332,9) * 2332 + 2332 + 1 is prime

    repeat(332,18) * 2332 + 2332 + 1 is prime

    repeat(332,62) * 2332 + 1 is prime

    repeat(332,68) + 1 is prime

    repeat(332,106) * 2332 - 2332 + 1 is prime

    repeat(332,141) * 2332 - 1 is prime

    repeat(332,153) * 2332 + 2332 + 1 is prime

    repeat(332,220) * 2332 - 332 - 1 is prime

    repeat(332,273) * 2332 + 1 is prime

    repeat(332,300) * 2332 - 1 is prime

  • 334
    334*2334 + 334 + 2334 - 1 is prime

  • 335
    repeat(335,3) * 2335 + 2335 - 1 is prime

    repeat(335,61) * 2335 + 1 is prime

    repeat(335,160) * 2335 + 1 is prime

    repeat(335,216) * 2335 - 2335 + 1 is prime

  • 336
    repeat(336,1) + 1 is prime

    repeat(336,2) * 2336 + 336 + 1 is prime

    repeat(336,4) + 1 is prime

    repeat(336,7) + 1 is prime

    repeat(336,13) * 2336 - 336 - 1 is prime

    repeat(336,19) + 1 is prime

    repeat(336,21) + 1 is prime

    repeat(336,24) + 1 is prime

    repeat(336,34) + 1 is prime

    repeat(336,36) * 2336 + 2336 + 1 is prime

    repeat(336,46) * 2336 + 336 - 1 is prime

    repeat(336,65) + 1 is prime

    repeat(336,94) + 1 is prime

    repeat(336,210) * 2336 + 336 + 1 is prime

    repeat(336,232) * 2336 - 336 + 1 is prime

    repeat(336,316) * 2336 + 2336 + 1 is prime

    repeat(336,325) * 2336 - 336 - 1 is prime

  • 339
    repeat(339,12) * 2339 - 1 is prime

    repeat(339,92) * 2339 + 1 is prime

    repeat(339,201) * 2339 - 1 is prime

    repeat(339,281) * 2339 - 1 is prime

    repeat(339,339) * 2339 - 1 is prime

  • 342
    repeat(342,2) + 1 is prime

    repeat(342,28) + 1 is prime

    repeat(342,32) * 2342 + 1 is prime

    repeat(342,35) * 2342 + 2342 + 1 is prime

    repeat(342,38) + 1 is prime

    repeat(342,41) * 2342 - 2342 - 1 is prime

    repeat(342,42) * 2342 - 1 is prime

    repeat(342,70) * 2342 - 1 is prime

    repeat(342,83) * 2342 - 1 is prime

    repeat(342,103) * 2342 - 1 is prime

    repeat(342,151) * 2342 + 342 + 1 is prime

    repeat(342,168) * 2342 + 1 is prime

    repeat(342,195) * 2342 + 2342 + 1 is prime

    repeat(342,203) * 2342 - 2342 - 1 is prime

    repeat(342,288) * 2342 + 1 is prime

  • 345
    345*2345 - 345 - 2345 is prime

  • 346
    repeat(346,1) + 1 is prime

    repeat(346,12) + 1 is prime

    repeat(346,43) * 2346 - 2346 - 1 is prime

    repeat(346,50) * 2346 - 1 is prime

    repeat(346,52) * 2346 - 2346 + 1 is prime

    repeat(346,53) * 2346 + 346 + 1 is prime

    repeat(346,57) * 2346 - 346 - 1 is prime

    repeat(346,78) * 2346 + 346 + 1 is prime

    repeat(346,129) + 1 is prime

    repeat(346,141) * 2346 - 2346 - 1 is prime

    repeat(346,143) * 2346 - 346 + 1 is prime

    repeat(346,148) * 2346 - 2346 + 1 is prime

    repeat(346,170) * 2346 - 1 is prime

    repeat(346,223) + 1 is prime

    repeat(346,230) * 2346 + 346 + 1 is prime

    repeat(346,238) * 2346 - 346 + 1 is prime

    repeat(346,240) * 2346 - 346 - 1 is prime

    repeat(346,287) * 2346 + 346 - 1 is prime

  • 348
    repeat(348,1) + 1 is prime

    repeat(348,10) * 2348 - 1 is prime

    repeat(348,18) * 2348 - 348 - 1 is prime

    repeat(348,31) * 2348 - 1 is prime

    repeat(348,59) * 2348 - 2348 - 1 is prime

    repeat(348,137) * 2348 - 1 is prime

    repeat(348,189) + 1 is prime

    repeat(348,254) * 2348 - 348 + 1 is prime

    repeat(348,330) * 2348 - 348 - 1 is prime

  • 349
    repeat(349,1) is prime

    repeat(349,9) * 2349 - 1 is prime

    repeat(349,21) * 2349 - 2349 + 1 is prime

    repeat(349,58) * 2349 - 1 is prime

    repeat(349,60) * 2349 + 1 is prime

    repeat(349,88) * 2349 - 2349 + 1 is prime

    repeat(349,111) * 2349 - 1 is prime

    repeat(349,286) * 2349 - 1 is prime

  • 350
    repeat(350,2) + 1 is prime

    repeat(350,16) * 2350 - 350 + 1 is prime

    repeat(350,32) * 2350 + 1 is prime

    repeat(350,38) * 2350 + 1 is prime

    repeat(350,73) * 2350 - 1 is prime

    repeat(350,78) * 2350 - 1 is prime

    repeat(350,160) * 2350 - 350 + 1 is prime

    repeat(350,166) * 2350 - 1 is prime

    repeat(350,265) * 2350 - 350 - 1 is prime

    repeat(350,291) * 2350 + 350 - 1 is prime

  • 351
    repeat(351,10) * 2351 + 1 is prime

    repeat(351,204) * 2351 + 1 is prime

    repeat(351,326) * 2351 + 1 is prime

  • 352
    repeat(352,1) + 1 is prime

    repeat(352,2) * 2352 + 2352 + 1 is prime

    repeat(352,4) * 2352 + 2352 - 1 is prime

    repeat(352,5) * 2352 - 2352 + 1 is prime

    repeat(352,5) * 2352 + 2352 - 1 is prime

    repeat(352,7) + 1 is prime

    repeat(352,39) + 1 is prime

    repeat(352,114) + 1 is prime

    repeat(352,173) * 2352 - 2352 + 1 is prime

    repeat(352,242) * 2352 - 1 is prime

    repeat(352,264) * 2352 + 2352 + 1 is prime

    repeat(352,316) * 2352 - 2352 + 1 is prime

    repeat(352,336) * 2352 + 1 is prime

  • 354
    repeat(354,14) * 2354 - 354 - 1 is prime

    repeat(354,18) * 2354 + 1 is prime

    repeat(354,35) * 2354 - 2354 - 1 is prime

    repeat(354,42) * 2354 + 1 is prime

    repeat(354,46) * 2354 + 1 is prime

    repeat(354,65) * 2354 + 354 + 1 is prime

    repeat(354,109) * 2354 - 354 + 1 is prime

    repeat(354,117) * 2354 - 2354 - 1 is prime

    repeat(354,122) * 2354 + 1 is prime

    repeat(354,139) * 2354 + 2354 + 1 is prime

    repeat(354,144) * 2354 + 354 + 1 is prime

    repeat(354,220) * 2354 - 354 + 1 is prime

    repeat(354,289) * 2354 + 354 + 1 is prime

  • 356
    repeat(356,18) + 1 is prime

    repeat(356,20) + 1 is prime

    repeat(356,35) * 2356 - 2356 - 1 is prime

    repeat(356,42) * 2356 + 2356 + 1 is prime

    repeat(356,129) * 2356 - 2356 - 1 is prime

    repeat(356,178) * 2356 + 2356 + 1 is prime

    repeat(356,218) * 2356 - 2356 + 1 is prime

    repeat(356,280) * 2356 + 2356 + 1 is prime

    repeat(356,323) * 2356 + 356 + 1 is prime

    repeat(356,348) * 2356 + 1 is prime

  • 357
    repeat(357,8) * 2357 - 1 is prime

    repeat(357,26) * 2357 - 1 is prime

    repeat(357,35) * 2357 - 1 is prime

    repeat(357,105) * 2357 - 1 is prime

    repeat(357,197) * 2357 - 1 is prime

    repeat(357,232) * 2357 - 1 is prime

  • 358
    repeat(358,1) + 1 is prime

    repeat(358,12) + 1 is prime

    repeat(358,19) * 2358 + 1 is prime

    repeat(358,34) * 2358 - 2358 + 1 is prime

    repeat(358,58) * 2358 - 2358 + 1 is prime

    repeat(358,96) * 2358 + 358 + 1 is prime

    repeat(358,112) * 2358 + 1 is prime

    repeat(358,155) * 2358 - 2358 + 1 is prime

    repeat(358,303) + 1 is prime

  • 360
    repeat(360,3) + 1 is prime

    repeat(360,4) * 2360 + 360 - 1 is prime

    repeat(360,6) + 1 is prime

    repeat(360,7) * 2360 - 360 + 1 is prime

    repeat(360,11) + 1 is prime

    repeat(360,17) + 1 is prime

    repeat(360,28) * 2360 + 360 + 1 is prime

    repeat(360,44) + 1 is prime

    repeat(360,48) * 2360 + 1 is prime

    repeat(360,76) + 1 is prime

    repeat(360,87) * 2360 - 360 - 1 is prime

    repeat(360,99) * 2360 - 2360 - 1 is prime

    repeat(360,136) * 2360 - 2360 - 1 is prime

    repeat(360,146) * 2360 + 1 is prime

    repeat(360,152) * 2360 - 360 - 1 is prime

    repeat(360,154) * 2360 - 2360 - 1 is prime

    repeat(360,185) * 2360 - 1 is prime

    repeat(360,194) * 2360 + 360 + 1 is prime

    repeat(360,274) * 2360 + 1 is prime

    repeat(360,297) + 1 is prime

    repeat(360,360) * 2360 + 360 - 1 is prime

  • 361
    repeat(361,12) * 2361 - 2361 + 1 is prime

    repeat(361,63) * 2361 + 1 is prime

    repeat(361,66) * 2361 + 1 is prime

  • 362
    362*2362 - 1 is prime

  • 364
    repeat(364,16) * 2364 - 2364 + 1 is prime

    repeat(364,29) * 2364 - 364 + 1 is prime

    repeat(364,37) * 2364 - 2364 - 1 is prime

    repeat(364,114) * 2364 + 364 + 1 is prime

    repeat(364,145) * 2364 - 364 - 1 is prime

    repeat(364,271) * 2364 - 364 + 1 is prime

    repeat(364,350) * 2364 + 364 + 1 is prime

  • 365
    repeat(365,42) * 2365 + 2365 - 1 is prime

    repeat(365,246) * 2365 - 1 is prime

  • 366
    repeat(366,1) + 1 is prime

    repeat(366,7) + 1 is prime

    repeat(366,7) * 2366 - 366 - 1 is prime

    repeat(366,8) * 2366 - 366 - 1 is prime

    repeat(366,11) + 1 is prime

    repeat(366,11) * 2366 + 2366 + 1 is prime

    repeat(366,17) + 1 is prime

    repeat(366,18) * 2366 - 1 is prime

    repeat(366,32) + 1 is prime

    repeat(366,33) + 1 is prime

    repeat(366,35) * 2366 + 366 + 1 is prime

    repeat(366,37) + 1 is prime

    repeat(366,46) * 2366 - 1 is prime

    repeat(366,50) * 2366 - 366 + 1 is prime

    repeat(366,55) * 2366 + 2366 + 1 is prime

    repeat(366,109) + 1 is prime

    repeat(366,116) * 2366 - 366 + 1 is prime

    repeat(366,139) * 2366 + 366 - 1 is prime

    repeat(366,195) * 2366 - 1 is prime

    repeat(366,281) * 2366 - 366 - 1 is prime

    repeat(366,297) + 1 is prime

    repeat(366,320) * 2366 - 366 - 1 is prime

  • 365
    repeat(365,42) * 2365 + 2365 - 1 is prime

    repeat(365,246) * 2365 - 1 is prime

  • 366
    repeat(366,1) + 1 is prime

    repeat(366,7) + 1 is prime

    repeat(366,7) * 2366 - 366 - 1 is prime

    repeat(366,8) * 2366 - 366 - 1 is prime

    repeat(366,11) + 1 is prime

    repeat(366,11) * 2366 + 2366 + 1 is prime

    repeat(366,17) + 1 is prime

    repeat(366,18) * 2366 - 1 is prime

    repeat(366,32) + 1 is prime

    repeat(366,33) + 1 is prime

    repeat(366,35) * 2366 + 366 + 1 is prime

    repeat(366,37) + 1 is prime

    repeat(366,46) * 2366 - 1 is prime

    repeat(366,50) * 2366 - 366 + 1 is prime

    repeat(366,55) * 2366 + 2366 + 1 is prime

    repeat(366,109) + 1 is prime

    repeat(366,116) * 2366 - 366 + 1 is prime

    repeat(366,139) * 2366 + 366 - 1 is prime

    repeat(366,195) * 2366 - 1 is prime

    repeat(366,281) * 2366 - 366 - 1 is prime

    repeat(366,297) + 1 is prime

    repeat(366,320) * 2366 - 366 - 1 is prime

  • 367
    repeat(367,1) is prime

    repeat(367,6) * 2367 + 1 is prime

    repeat(367,10) * 2367 - 2367 - 1 is prime

    repeat(367,244) * 2367 - 2367 - 1 is prime

    repeat(367,284) * 2367 + 1 is prime

  • 368
    repeat(368,2) + 1 is prime

    repeat(368,3) + 1 is prime

    repeat(368,5) + 1 is prime

    repeat(368,11) * 2368 - 368 - 1 is prime

    repeat(368,14) * 2368 - 2368 + 1 is prime

    repeat(368,15) + 1 is prime

    repeat(368,19) * 2368 - 368 - 1 is prime

    repeat(368,24) + 1 is prime

    repeat(368,42) + 1 is prime

    repeat(368,49) * 2368 + 2368 - 1 is prime

    repeat(368,121) * 2368 - 1 is prime

    repeat(368,137) + 1 is prime

    repeat(368,172) * 2368 - 1 is prime

    repeat(368,284) * 2368 + 1 is prime

    repeat(368,344) * 2368 + 368 + 1 is prime

    repeat(368,344) * 2368 - 2368 + 1 is prime

  • 369
    repeat(369,13) * 2369 - 1 is prime

    repeat(369,21) * 2369 - 1 is prime

    repeat(369,56) * 2369 - 1 is prime

    repeat(369,115) * 2369 + 2369 - 1 is prime

    repeat(369,362) * 2369 - 1 is prime

  • 370
    repeat(370,4) + 1 is prime

    repeat(370,82) + 1 is prime

  • 372
    repeat(372,1) + 1 is prime

    repeat(372,6) + 1 is prime

    repeat(372,9) * 2372 - 372 + 1 is prime

    repeat(372,18) * 2372 + 1 is prime

    repeat(372,20) * 2372 - 372 - 1 is prime

    repeat(372,67) * 2372 + 1 is prime

    repeat(372,100) + 1 is prime

    repeat(372,126) * 2372 - 1 is prime

    repeat(372,137) * 2372 - 372 + 1 is prime

    repeat(372,148) * 2372 - 1 is prime

    repeat(372,340) + 1 is prime

  • 374
    repeat(374,8) * 2374 + 374 + 1 is prime

    repeat(374,14) * 2374 - 374 - 1 is prime

    repeat(374,18) * 2374 + 2374 + 1 is prime

    repeat(374,25) * 2374 - 374 - 1 is prime

    repeat(374,37) * 2374 - 374 + 1 is prime

    repeat(374,37) * 2374 + 2374 - 1 is prime

    repeat(374,47) * 2374 + 1 is prime

    repeat(374,47) * 2374 - 2374 + 1 is prime

    repeat(374,62) * 2374 + 1 is prime

    repeat(374,82) * 2374 - 374 - 1 is prime

    repeat(374,107) * 2374 + 1 is prime

    repeat(374,137) * 2374 - 2374 + 1 is prime

    repeat(374,177) * 2374 - 374 + 1 is prime

    repeat(374,205) * 2374 - 374 + 1 is prime

    repeat(374,283) * 2374 - 374 - 1 is prime

    repeat(374,340) * 2374 - 374 + 1 is prime

  • 385
    repeat(385,75) * 2385 + 1 is prime

    repeat(385,96) * 2385 - 1 is prime

    repeat(385,228) * 2385 - 2385 + 1 is prime

  • 377
    repeat(377,9) * 2377 - 1 is prime

    repeat(377,95) * 2377 - 1 is prime

    repeat(377,182) * 2377 - 1 is prime

    repeat(377,273) * 2377 - 1 is prime

  • 378
    repeat(378,1) + 1 is prime

    repeat(378,2) + 1 is prime

    repeat(378,2) * 2378 + 1 is prime

    repeat(378,3) + 1 is prime

    repeat(378,6) + 1 is prime

    repeat(378,9) + 1 is prime

    repeat(378,13) + 1 is prime

    repeat(378,22) * 2378 - 1 is prime

    repeat(378,25) + 1 is prime

    repeat(378,33) * 2378 + 2378 + 1 is prime

    repeat(378,53) * 2378 + 2378 + 1 is prime

    repeat(378,55) + 1 is prime

    repeat(378,64) + 1 is prime

    repeat(378,70) * 2378 - 378 - 1 is prime

    repeat(378,87) * 2378 + 378 + 1 is prime

    repeat(378,114) * 2378 - 1 is prime

    repeat(378,203) * 2378 + 2378 + 1 is prime

    repeat(378,246) * 2378 - 378 - 1 is prime

    repeat(378,273) * 2378 - 378 - 1 is prime

    repeat(378,330) * 2378 - 378 - 1 is prime

  • 380
    repeat(380,8) + 1 is prime

    repeat(380,35) * 2380 + 380 + 1 is prime

    repeat(380,38) + 1 is prime

    repeat(380,62) * 2380 - 380 - 1 is prime

    repeat(380,66) * 2380 - 1 is prime

    repeat(380,72) + 1 is prime

    repeat(380,245) * 2380 - 2380 - 1 is prime

    repeat(380,323) * 2380 + 1 is prime

  • 381
    repeat(381,19) * 2381 + 2381 - 1 is prime

    repeat(381,29) * 2381 + 1 is prime

    repeat(381,30) * 2381 + 1 is prime

    repeat(381,31) * 2381 + 2381 - 1 is prime

  • 382
    repeat(382,1) + 1 is prime

    repeat(382,26) * 2382 - 1 is prime

    repeat(382,39) + 1 is prime

    repeat(382,54) * 2382 - 2382 - 1 is prime

    repeat(382,74) * 2382 + 382 - 1 is prime

    repeat(382,100) * 2382 + 382 - 1 is prime

    repeat(382,101) * 2382 + 2382 - 1 is prime

    repeat(382,103) * 2382 - 382 + 1 is prime

    repeat(382,108) * 2382 + 2382 + 1 is prime

    repeat(382,126) * 2382 - 2382 - 1 is prime

    repeat(382,170) * 2382 - 382 + 1 is prime

    repeat(382,202) * 2382 - 2382 - 1 is prime

    repeat(382,246) + 1 is prime

    repeat(382,301) * 2382 + 382 - 1 is prime

  • 384
    repeat(384,1) * 2384 - 1 is prime

    384*2384 - 1 is prime

    repeat(384,22) * 2384 - 384 + 1 is prime

    repeat(384,27) * 2384 - 384 + 1 is prime

    repeat(384,47) * 2384 - 1 is prime

    repeat(384,79) * 2384 + 2384 + 1 is prime

    repeat(384,82) * 2384 - 384 + 1 is prime

    repeat(384,87) * 2384 + 384 + 1 is prime

    repeat(384,177) * 2384 - 1 is prime

    repeat(384,198) * 2384 + 2384 + 1 is prime

    repeat(384,215) * 2384 - 1 is prime

    repeat(384,367) * 2384 + 384 + 1 is prime

  • 385
    repeat(385,75) * 2385 + 1 is prime

    repeat(385,96) * 2385 - 1 is prime

    repeat(385,228) * 2385 - 2385 + 1 is prime

  • 386
    repeat(386,11) + 1 is prime

    repeat(386,13) * 2386 - 386 + 1 is prime

    repeat(386,20) + 1 is prime

    repeat(386,21) + 1 is prime

    repeat(386,28) * 2386 - 2386 + 1 is prime

    repeat(386,41) + 1 is prime

    repeat(386,48) * 2386 - 1 is prime

    repeat(386,55) * 2386 + 2386 + 1 is prime

    repeat(386,63) * 2386 + 386 - 1 is prime

    repeat(386,137) * 2386 - 2386 - 1 is prime

    repeat(386,215) * 2386 - 2386 - 1 is prime

    repeat(386,231) * 2386 + 386 - 1 is prime

    repeat(386,295) * 2386 - 2386 + 1 is prime

    repeat(386,320) * 2386 + 386 + 1 is prime

  • 387
    repeat(387,13) * 2387 + 1 is prime

    repeat(387,61) * 2387 - 2387 + 1 is prime

    repeat(387,99) * 2387 + 2387 - 1 is prime

    repeat(387,234) * 2387 + 1 is prime

    repeat(387,339) * 2387 - 2387 + 1 is prime

  • 388
    repeat(388,1) + 1 is prime

    repeat(388,12) * 2388 - 2388 - 1 is prime

    repeat(388,18) * 2388 + 388 + 1 is prime

    repeat(388,33) + 1 is prime

    repeat(388,37) * 2388 - 2388 - 1 is prime

    repeat(388,40) + 1 is prime

    repeat(388,53) * 2388 - 2388 + 1 is prime

    repeat(388,61) * 2388 - 388 + 1 is prime

    repeat(388,102) * 2388 + 388 + 1 is prime

    repeat(388,103) * 2388 - 388 - 1 is prime

    repeat(388,207) * 2388 - 388 - 1 is prime

    repeat(388,224) * 2388 + 388 + 1 is prime

    repeat(388,236) * 2388 - 2388 + 1 is prime

    repeat(388,273) * 2388 - 1 is prime

    repeat(388,281) * 2388 - 2388 + 1 is prime

  • 389
    repeat(389,1) is prime

    repeat(389,24) * 2389 + 2389 - 1 is prime

    repeat(389,60) * 2389 + 2389 - 1 is prime

    repeat(389,136) * 2389 + 2389 - 1 is prime

    repeat(389,340) * 2389 + 2389 - 1 is prime

  • 390
    repeat(390,2) + 1 is prime

    repeat(390,6) * 2390 + 1 is prime

    repeat(390,14) + 1 is prime

    repeat(390,20) * 2390 + 390 + 1 is prime

    repeat(390,24) * 2390 - 390 + 1 is prime

    repeat(390,34) * 2390 + 1 is prime

    repeat(390,111) * 2390 - 390 - 1 is prime

    repeat(390,144) * 2390 + 390 - 1 is prime

    repeat(390,171) * 2390 - 1 is prime

    repeat(390,231) + 1 is prime

    repeat(390,231) * 2390 + 390 - 1 is prime

    repeat(390,280) + 1 is prime

    repeat(390,338) * 2390 - 390 - 1 is prime

    repeat(390,375) * 2390 - 390 + 1 is prime

  • 391
    repeat(391,16) * 2391 + 2391 + 1 is prime

    repeat(391,50) * 2391 - 2391 - 1 is prime

    repeat(391,204) * 2391 - 1 is prime

    repeat(391,364) * 2391 - 1 is prime

  • 392
    repeat(392,21) + 1 is prime

    repeat(392,27) + 1 is prime

    repeat(392,46) * 2392 - 1 is prime

    repeat(392,99) + 1 is prime

    repeat(392,107) * 2392 + 392 - 1 is prime

    repeat(392,166) * 2392 - 1 is prime

  • 393
    repeat(393,118) * 2393 + 1 is prime

    repeat(393,155) * 2393 + 1 is prime

    repeat(393,354) * 2393 + 1 is prime

  • 394
    repeat(394,2) * 2394 + 2394 - 1 is prime

    repeat(394,12) * 2394 + 394 + 1 is prime

    repeat(394,25) * 2394 + 394 - 1 is prime

    repeat(394,74) * 2394 - 394 + 1 is prime

    repeat(394,264) * 2394 - 394 - 1 is prime

    repeat(394,369) * 2394 - 2394 - 1 is prime

    repeat(394,371) * 2394 + 394 - 1 is prime

  • 395
    repeat(395,18) * 2395 - 2395 + 1 is prime

    repeat(395,35) * 2395 + 2395 + 1 is prime

    repeat(395,138) * 2395 - 2395 + 1 is prime

    repeat(395,318) * 2395 - 2395 + 1 is prime

  • 396
    396*2396 - 396 - 2396 - 1 is prime

  • 397
    repeat(397,1) is prime

    repeat(397,54) * 2397 - 1 is prime

  • 398
    repeat(398,9) * 2398 + 2398 + 1 is prime

    repeat(398,120) * 2398 + 1 is prime

    repeat(398,139) * 2398 - 1 is prime

    repeat(398,153) * 2398 + 2398 + 1 is prime

    repeat(398,159) * 2398 - 2398 - 1 is prime

    repeat(398,191) * 2398 + 398 + 1 is prime

    repeat(398,222) * 2398 + 1 is prime

    repeat(398,273) * 2398 + 2398 + 1 is prime

  • 412
    412*2412 + 412 + 2412 - 1 is prime

  • 423
    423*2423 - 423 + 2423 is prime

  • 426
    426*2426 + 426 + 1 is prime

  • 439
    439*2439 + 439 + 2439 is prime

  • 462
    462*2462 - 1 is prime

  • 478
    478*2478 - 478 - 1 is prime

  • 483
    483*2483 + 483 - 2483 is prime

  • 500
    500*2500 - 500 - 2500 - 1 is prime

  • 512
    512*2512 - 1 is prime

  • 563
    563*2563 + 563 - 2563 is prime

  • 565
    565*2565 + 565 + 2565 is prime

  • 574
    574*2574 - 574 + 1 is prime

  • 600
    600*2600 - 600 + 1 is prime

  • 604
    604*2604 - 604 - 1 is prime

  • 621
    621*2621 - 621 - 2621 is prime

  • 628
    628*2628 - 628 + 1 is prime

  • 634
    634*2634 - 634 - 1 is prime

  • 705
    705*2705 - 705 - 2705 is prime

  • 749
    749*2749 + 749 + 2749 is prime

  • 790
    790*2790 - 790 - 1 is prime

  • 822
    822*2822 - 1 is prime

  • 844
    844*2844 - 844 - 2844 - 1 is prime

  • 868
    868*2868 - 868 - 1 is prime

  • 902
    902*2902 + 902 + 2902 - 1 is prime

  • 987
    978*2978 + 978 + 1 is prime

  • 1015
    1015*21015 + 1015 - 21015 is prime

  • 1106
    1106*21106 + 1106 + 21106 - 1 is prime

  • 1120
    1120*21120 + 1120 - 1 is prime

  • 1264
    1264*21264 - 1264 - 1 is prime

  • 1364
    1364*21364 + 1364 + 21364 - 1 is prime

  • 1376
    1376*21376 - 1376 - 1 is prime

  • 1438
    1438*21438 + 1438 - 1 is prime

  • 1530
    1530*21530 + 1530 + 1 is prime

  • 1600
    1600*21600 - 1600 + 1 is prime

  • 1613
    16132 = 867253 + 867257 + 867259 (3 consecutive primes) = 25247 + 25253 + ... + 26251 + 26261 (101 consecutive primes)

    1613 is a prime such that the previous two primes AND the next two primes are twin primes

    There are 1613 prime sextuplets (p, p+4, p+6, p+10, p+12, p+16 all prime) < 1010

    1613 is the 17th prime in the prime sequence f(n)=4*n2 - 4*n + 653
    Note that f(0), f(1), ... , f(16), f(17), f(18) are all primes, while f(19) is not.
    (760*101613 - 31)/9 = 8 repeat(4,1613) 1 is prime
    Note the 1613 consecutive 4 preceded by an 8 and followed by a 1
    given p2=1613 and the previous prime p1=1609 it is curious that p12 + p23 ± 1 is a twin prime pair

    821613 - 811613 is prime

    1613 is the smallest 4 digit prime that starts a run of 6 consecutive primes where between primes exactly one digit changes and where the resulting digits may be permuted
    I.e., 1613, 1619, 1621, 1627, 1637, 1657
    1613 is the largest prime factor of 226+1

    π(1613) = 28-1

    π(1613) + 2*1619 is a perfect square of a prime
    I.e., 592
  • 1630
    1630*21630 + 1630 - 21630 + 1 is prime

  • 1637
    1637*21637 + 1637 + 21637 is prime

  • 2161
    2161*22161 + 2161 - 22161 is prime

  • 2192
    2192*22192 + 2192 - 22192 + 1 is prime

  • 2339
    2339*22339 + 2339 - 22339 is prime

  • 2536
    2536*22536 - 2536 - 1 is prime

  • 2800
    2800*22800 - 2800 + 1 is prime

  • 2812
    2812*22812 + 2812 + 22812 - 1 is prime

  • 2957
    2957*22957 - 2957 + 22957 is prime

  • 2974
    2974*22974 + 2974 + 22974 - 1 is prime

  • 3236
    3236*23236 + 3236 + 23236 - 1 is prime

  • 3370
    3370*23370 + 3370 - 1 is prime

  • 3396
    3396*23396 - 3396 + 1 is prime

  • 3544
    3544*23544 - 3544 - 1 is prime

  • 3696
    3696*23696 - 3696 - 23696 - 1 is prime

  • 3913
    3913*23913 + 3913 + 23913 is prime

  • 4736
    4736*24736 + 4736 + 24736 - 1 is prime

  • 4822
    4822*24822 + 4822 + 24822 - 1 is prime

  • 4885
    4885*24885 - 4885 - 24885 is prime

  • 5052
    5052*25052 - 5052 - 25052 - 1 is prime

  • 5062
    5062*25062 + 5062 - 1 is prime

  • 5066
    5066*25066 + 5066 - 25066 + 1 is prime

  • 5125
    5125*25125 - 5125 - 25125 is prime

  • 5268
    5268*25268 + 5268 + 1 is prime

  • 5312
    5312*25312 - 1 is prime

  • 5328
    5328*25328 - 5328 - 25328 - 1 is prime

  • 6300
    6300*26300 - 6300 - 26300 - 1 is prime

  • 6322
    6322*26322 + 6322 - 26322 + 1 is prime

  • 6564
    6564*26564 - 6564 - 1 is prime

  • 6607
    6607*26607 - 6607 - 26607 is prime

  • 6714
    6714*26714 + 6714 - 1 is prime

  • 6790
    6790*26790 + 6790 + 26790 - 1 is prime

  • 6956
    6956*26956 + 6956 - 26956 + 1 is prime

  • 7238
    7238*27238 + 7238 + 1 is prime

  • 7268
    7268*27268 - 7268 - 1 is prime

  • 7328
    7328*27328 + 7328 + 27328 - 1 is prime

  • 7726
    7726*27726 + 7726 + 27726 - 1 is prime

  • 7780
    7780*27780 - 7780 - 1 is prime

  • 7989
    7989*27989 - 7989 + 27989 is prime

  • 8366
    8366*28366 - 8366 - 1 is prime

  • 8384
    8384*28384 + 8384 + 1 is prime

  • 8892
    8892*28892 - 8892 + 1 is prime

  • 9426
    9426*29426 - 9426 + 1 is prime

  • 9436
    9436*29436 + 9436 - 1 is prime

  • 9542
    9542*29542 + 9542 + 29542 - 1 is prime

  • 9605
    9605*29605 + 9605 + 29605 is prime

  • 9696
    9696*29696 + 9696 + 1 is prime

  • (37*102883-73)/99
    repeat(37,1441) * 10 + 3 is prime (see the 37 SUPP prime)

Definition:

repeat(v, n) = v{repeated n times}

For example:

repeat(309,4) = 309309309309

If can be shown that:

repeat(v, n) = v * (10(d*n)-1)/(10d-1)

where ''v'' is ''d'' digits in length.


You can use the calc program to compute the decimal values of the above curious numbers.

The following calc function may be used for the repeat(v, n) function:

/*
 * repeat - depeat a set of digits
 *
 * given:
 *      v  digit set to repeat
 *      n   repeat count
 */
define repeat(v,n)
{
    local digcnt;

    digcnt = digits(v);

    return v * (10^(digcnt*n)-1) / (10^digcnt-1);
}


Some useful links

Mersenne primes

Definitions and theory

Source code

  • Calc: able to compute decimal values primes
  • Number: able to compute English names of primes
  • GIMPS code: has been used to prove primality of some Mersenne numbers
  • GIMPS search credits and thank yous

Misc prime links



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$Revision: 7.4 $ $Date: 2014/02/10 02:38:20 $