
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*2^{3}  3  2^{3} is prime
3*2^{3}  3 + 2^{3} is prime
3*2^{3} + 3  2^{3} is prime
 4
4*2^{4}  4  1 is prime
4*2^{4}  4 + 1 is prime
4*2^{4}  4  2^{4}  1 is prime
4*2^{4} + 4  1 is prime
4*2^{4} + 4  2^{4} + 1 is prime
4*2^{4} + 4 + 2^{4}  1 is prime
 5
5*2^{5} + 5 + 2^{5} is prime
 6
6*2^{6}  1 is prime
6*2^{6}  6 + 1 is prime
6*2^{6}  6  2^{6}  1 is prime
6*2^{6} + 6  1 is prime
 7
7*2^{7}  7  2^{7} is prime
7*2^{7} + 7 + 2^{7} is prime
 8
8*2^{8}  8  1 is prime
8*2^{8}  8  2^{8}  1 is prime
8*2^{8} + 8  2^{8} + 1 is prime
8*2^{8} + 8 + 2^{8}  1 is prime
 10
10*2^{10} + 10  2^{10} + 1 is prime
10*2^{10} + 10 + 2^{10}  1 is prime
 12
12*2^{12}  12  1 is prime
 13
13*2^{13} + 13  2^{13} is prime
 16
16*2^{16}  16  1 is prime
 17
17*2^{17} + 17  2^{17} is prime
 18
18*2^{18}  18  2^{18}  1 is prime
 19
19*2^{19} + 19  2^{19} is prime
19*2^{19} + 19 + 2^{19} is prime
 20
20*2^{20}  20  2^{20}  1 is prime
 21
21*2^{21} + 21  2^{21} is prime
 22
22*2^{22} + 22  2^{22} + 1 is prime
 27
27*2^{27} + 27 + 2^{27} is prime
 28
28*2^{28} + 28 + 2^{28}  1 is prime
 30
30*2^{30}  1 is prime
30*2^{30}  30 + 1 is prime
30*2^{30} + 30  1 is prime
 31
31*2^{31} + 31 + 2^{31} is prime
 32
32*2^{32}  1 is prime
32*2^{32}  32 + 1 is prime
 33
33*2^{33} + 33 + 2^{33} is prime
 34
34*2^{34} + 34  1 is prime
 37
37*2^{37} + 37 + 2^{37} is prime
 38
38*2^{38} + 38 + 1 is prime
 40
40*2^{40}  40  1 is prime
 42
42*2^{42}  42 + 1 is prime
 44
44*2^{44} + 44 + 2^{44}  1 is prime
 45
45*2^{45}  45  2^{45} is prime
 46
46*2^{46} + 46 + 2^{46}  1 is prime
 48
48*2^{48}  48  2^{48}  1 is prime
 54
The sum of the nonprime 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.
13^{54} + 54 is prime.
 56
Sigma(56) equals the first prime of the form 6n  1 factorial, 5!
2^{56}  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) = 2^{4} and 57^{57}  pi(57) is prime.
57 * 2^{25}  1 is prime.
57*2^{57}  57 + 2^{57} is prime
 58
58*2^{58} + 58  2^{58} + 1 is prime
 62
62*2^{62}  62  2^{62}  1 is prime
 64
64*2^{64} + 64  2^{64} + 1 is prime
 75
75*2^{75}  75  2^{75} is prime
 76
76*2^{76} + 76  2^{76} + 1 is prime
 80
80*2^{80}  80  1 is prime
 81
81*2^{81}  81  2^{81} is prime
 87
87*2^{87}  87  2^{87} is prime
 92
92*2^{92}  92  2^{92}  1 is prime
92*2^{92} + 92  2^{92} + 1 is prime
 94
94*2^{94} + 94  1 is prime
94*2^{94} + 94  2^{94} + 1 is prime
 111
111 * 2^{111}  111  2^{111} is prime.
 112
112*2^{112}  112  2^{112}  1 is prime
112*2^{112} + 112  2^{112} + 1 is prime
 113
113*2^{113} + 113 + 2^{113} is prime
 115
115*2^{115}  115  2^{115} is prime
 120
120*2^{120}  120 + 1 is prime
120*2^{120}  120  2^{120}  1 is prime
 122
122*2^{122} + 122  2^{122} + 1 is prime
 123
123 * 2^{123}  1 is prime.
 127
2^{21271}1 has no prime factors less than 5 * 10^{50}.
 173
173*2^{173} + 173 + 2^{173} is prime
 179
179*2^{179} + 179  2^{179} is prime
 182
182*2^{182}  182  2^{182}  1 is prime
 210
210*2^{210}  210 + 1 is prime
 212
212*2^{212}  212  2^{212}  1 is prime
 216
216*2^{216} + 216  1 is prime
 217
217*2^{217} + 217  2^{217} is prime
 218
218*2^{218} + 218 + 2^{218}  1 is prime
 225
225*2^{225}  225  2^{225} is prime
 232
232*2^{232} + 232 + 2^{232}  1 is prime
 248
248*2^{248}  248 + 1 is prime
 256
256 = (21701  19937)  (23209  21701). Note the use of three consecutive Mersenne prime exponents!
 274
274*2^{274} + 274  2^{274} + 1 is prime
 284
284*2^{284}  284 + 1 is prime
 286
repeat(286,8) * 2^{286}  1 is prime
repeat(286,22) * 2^{286} + 286  1 is prime
repeat(286,57) * 2^{286} + 2^{286} + 1 is prime
repeat(286,114) * 2^{286}  2^{286}  1 is prime
repeat(286,155) * 2^{286} + 2^{286} + 1 is prime
 287
repeat(287,60) * 2^{287} + 1 is prime
repeat(287,109) * 2^{287} + 1 is prime
repeat(287,110) * 2^{287}  2^{287}  1 is prime
repeat(287,118) * 2^{287}  2^{287}  1 is prime
 288
repeat(288,6) + 1 is prime
repeat(288,24) + 1 is prime
repeat(288,34) * 2^{288}  1 is prime
repeat(288,48) * 2^{288}  1 is prime
repeat(288,68) * 2^{288} + 288 + 1 is prime
repeat(288,70) + 1 is prime
repeat(288,98) + 1 is prime
repeat(288,149) * 2^{288}  288 + 1 is prime
repeat(288,171) + 1 is prime
 290
repeat(290,1) * 2^{290} + 2^{290}  1 is prime
repeat(290,6) + 1 is prime
repeat(290,30) * 2^{290}  290 + 1 is prime
repeat(290,59) * 2^{290}  290  1 is prime
repeat(290,68) * 2^{290} + 290  1 is prime
repeat(290,73) * 2^{290}  290  1 is prime
repeat(290,131) * 2^{290} + 1 is prime
repeat(290,133) * 2^{290}  290  1 is prime
repeat(290,176) * 2^{290}  290  1 is prime
repeat(290,180) * 2^{290} + 1 is prime
 294
repeat(294,1) * 2^{294} + 2^{294} + 1 is prime
repeat(294,7) * 2^{294} + 1 is prime
repeat(294,11) * 2^{294}  294  1 is prime
repeat(294,55) * 2^{294} + 1 is prime
repeat(294,182) * 2^{294} + 1 is prime
repeat(294,247) * 2^{294} + 2^{294} + 1 is prime
 295
repeat(295,12) * 2^{295} + 1 is prime
repeat(295,41) * 2^{295}  2^{295}  1 is prime
repeat(295,117) * 2^{295}  2^{295} + 1 is prime
repeat(295,241) * 2^{295}  1 is prime
repeat(295,264) * 2^{295} + 2^{295}  1 is prime
 296
repeat(296,6) + 1 is prime
repeat(296,22) * 2^{296}  296 + 1 is prime
repeat(296,32) * 2^{296} + 296  1 is prime
repeat(296,46) * 2^{296}  296 + 1 is prime
repeat(296,50) * 2^{296} + 296  1 is prime
repeat(296,79) * 2^{296} + 296 + 1 is prime
repeat(296,109) * 2^{296} + 2^{296} + 1 is prime
repeat(296,154) * 2^{296} + 2^{296}  1 is prime
repeat(296,190) * 2^{296}  2^{296} + 1 is prime
repeat(296,281) * 2^{296} + 296 + 1 is prime
 297
repeat(297,57) * 2^{297}  1 is prime
repeat(297,67) * 2^{297}  2^{297} + 1 is prime
 298
repeat(298,3) * 2^{298}  298  1 is prime
repeat(298,7) * 2^{298} + 1 is prime
repeat(298,208) * 2^{298} + 1 is prime
repeat(298,220) * 2^{298}  2^{298} + 1 is prime
 300
repeat(300,2) + 1 is prime
repeat(300,3) * 2^{300}  2^{300}  1 is prime
repeat(300,6) + 1 is prime
repeat(300,13) * 2^{300} + 2^{300} + 1 is prime
repeat(300,18) * 2^{300} + 2^{300} + 1 is prime
repeat(300,30) + 1 is prime
repeat(300,33) * 2^{300}  300  1 is prime
repeat(300,42) * 2^{300}  1 is prime
repeat(300,46) * 2^{300} + 1 is prime
repeat(300,51) * 2^{300}  300  1 is prime
repeat(300,92) * 2^{300} + 2^{300} + 1 is prime
repeat(300,128) * 2^{300}  1 is prime
repeat(300,143) * 2^{300} + 300 + 1 is prime
repeat(300,235) * 2^{300}  300 + 1 is prime
repeat(300,237) * 2^{300} + 2^{300} + 1 is prime
repeat(300,259) * 2^{300}  2^{300}  1 is prime
 301
repeat(301,19) * 2^{301}  2^{301} + 1 is prime
repeat(301,24) * 2^{301} + 1 is prime
repeat(301,24) * 2^{301} + 2^{301}  1 is prime
repeat(301,48) * 2^{301} + 2^{301}  1 is prime
repeat(301,60) * 2^{301} + 1 is prime
repeat(301,60) * 2^{301}  2^{301} + 1 is prime
repeat(301,82) * 2^{301}  1 is prime
repeat(301,102) * 2^{301}  2^{301} + 1 is prime
repeat(301,120) * 2^{301}  1 is prime
 302
repeat(302,6) * 2^{302}  1 is prime
repeat(302,42) + 1 is prime
repeat(302,62) + 1 is prime
repeat(302,98) * 2^{302} + 2^{302}  1 is prime
repeat(302,128) * 2^{302} + 2^{302}  1 is prime
repeat(302,131) + 1 is prime
repeat(302,255) * 2^{302}  1 is prime
 303
repeat(303,99) * 2^{303}  1 is prime
 304
repeat(304,3) * 2^{304}  304  1 is prime
repeat(304,10) * 2^{304}  304 + 1 is prime
repeat(304,29) * 2^{304}  304 + 1 is prime
repeat(304,36) * 2^{304}  304  1 is prime
repeat(304,37) * 2^{304} + 304  1 is prime
repeat(304,54) * 2^{304} + 304 + 1 is prime
repeat(304,59) * 2^{304} + 304 + 1 is prime
repeat(304,67) * 2^{304}  304  1 is prime
repeat(304,73) * 2^{304}  2^{304}  1 is prime
repeat(304,75) * 2^{304} + 304 + 1 is prime
repeat(304,77) * 2^{304}  1 is prime
repeat(304,91) * 2^{304} + 304  1 is prime
repeat(304,134) * 2^{304}  2^{304} + 1 is prime
repeat(304,243) * 2^{304}  1 is prime
repeat(304,290) * 2^{304}  2^{304} + 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) * 2^{306} + 306  1 is prime
repeat(306,32) + 1 is prime
repeat(306,46) * 2^{306} + 306  1 is prime
repeat(306,47) * 2^{306}  1 is prime
repeat(306,77) * 2^{306}  2^{306}  1 is prime
repeat(306,90) * 2^{306}  306  1 is prime
repeat(306,111) * 2^{306}  306  1 is prime
repeat(306,129) + 1 is prime
repeat(306,149) + 1 is prime
repeat(306,152) * 2^{306} + 306  1 is prime
repeat(306,161) * 2^{306}  1 is prime
repeat(306,175) + 1 is prime
repeat(306,247) * 2^{306} + 306  1 is prime
repeat(306,285) + 1 is prime
 308
repeat(308,2) + 1 is prime
repeat(308,9) * 2^{308} + 1 is prime
repeat(308,30) * 2^{308} + 1 is prime
repeat(308,30) * 2^{308}  308 + 1 is prime
repeat(308,45) * 2^{308}  1 is prime
repeat(308,48) + 1 is prime
repeat(308,99) * 2^{308}  308 + 1 is prime
repeat(308,104) * 2^{308} + 2^{308}  1 is prime
repeat(308,117) * 2^{308}  308 + 1 is prime
repeat(308,160) * 2^{308} + 2^{308}  1 is prime
repeat(308,201) * 2^{308}  2^{308}  1 is prime
 309
repeat(309,4) * 2^{309} + 1 is prime
repeat(309,83) * 2^{309}  2^{309} + 1 is prime
repeat(309,141) * 2^{309} + 1 is prime
repeat(309,178) * 2^{309} + 1 is prime
 310
repeat(310,1) + 1 is prime
repeat(310,4) + 1 is prime
repeat(310,8) * 2^{310} + 310  1 is prime
repeat(310,16) * 2^{310} + 310  1 is prime
repeat(310,18) * 2^{310} + 1 is prime
repeat(310,28) + 1 is prime
repeat(310,36) * 2^{310} + 310 + 1 is prime
repeat(310,48) * 2^{310} + 310 + 1 is prime
repeat(310,57) + 1 is prime
repeat(310,61) * 2^{310}  310  1 is prime
repeat(310,73) + 1 is prime
repeat(310,104) * 2^{310}  310 + 1 is prime
repeat(310,132) * 2^{310} + 1 is prime
repeat(310,141) * 2^{310}  310  1 is prime
repeat(310,160) * 2^{310} + 310  1 is prime
repeat(310,173) * 2^{310}  310 + 1 is prime
repeat(310,182) * 2^{310} + 310 + 1 is prime
repeat(310,190) * 2^{310} + 1 is prime
repeat(310,295) * 2^{310} + 1 is prime
 312
repeat(312,1) + 1 is prime
repeat(312,2) + 1 is prime
repeat(312,20) * 2^{312}  1 is prime
repeat(312,26) + 1 is prime
repeat(312,29) + 1 is prime
repeat(312,51) * 2^{312} + 1 is prime
repeat(312,89) + 1 is prime
repeat(312,108) * 2^{312} + 1 is prime
repeat(312,174) * 2^{312} + 2^{312} + 1 is prime
repeat(312,198) * 2^{312}  312 + 1 is prime
repeat(312,223) * 2^{312}  312 + 1 is prime
repeat(312,232) + 1 is prime
repeat(312,241) + 1 is prime
repeat(312,259) * 2^{312}  312 + 1 is prime
 314
314*2^{314}  314  1 is prime
 315
repeat(315,15) * 2^{315}  1 is prime
repeat(315,18) * 2^{315} + 1 is prime
 316
repeat(316,1) + 1 is prime
repeat(316,7) + 1 is prime
repeat(316,7) * 2^{316} + 316  1 is prime
repeat(316,13) + 1 is prime
repeat(316,130) * 2^{316}  2^{316} + 1 is prime
repeat(316,286) * 2^{316}  2^{316} + 1 is prime
repeat(316,290) * 2^{316} + 2^{316} + 1 is prime
repeat(316,301) * 2^{316}  2^{316} + 1 is prime
repeat(316,309) + 1 is prime
 318
318*2^{318}  318  2^{318}  1 is prime
 321
repeat(321,56) * 2^{321} + 1 is prime
repeat(321,85) * 2^{321}  2^{321} + 1 is prime
repeat(321,117) * 2^{321} + 2^{321}  1 is prime
repeat(321,205) * 2^{321} + 2^{321}  1 is prime
 322
repeat(322,37) * 2^{322} + 322  1 is prime
repeat(322,153) * 2^{322} + 1 is prime
repeat(322,272) * 2^{322} + 322  1 is prime
repeat(322,302) * 2^{322} + 2^{322}  1 is prime
repeat(322,319) * 2^{322} + 2^{322}  1 is prime
 325
repeat(325,1) * 2^{325}  2^{325}  1 is prime
repeat(325,96) * 2^{325} + 2^{325}  1 is prime
 326
repeat(326,7) * 2^{326}  1 is prime
repeat(326,16) * 2^{326}  326  1 is prime
repeat(326,17) + 1 is prime
repeat(326,41) + 1 is prime
repeat(326,43) * 2^{326}  326 + 1 is prime
repeat(326,96) + 1 is prime
repeat(326,199) * 2^{326}  326 + 1 is prime
repeat(326,231) * 2^{326}  2^{326}  1 is prime
repeat(326,243) * 2^{326}  326 + 1 is prime
repeat(326,248) * 2^{326}  2^{326} + 1 is prime
repeat(326,269) * 2^{326}  2^{326}  1 is prime
 327
repeat(327,71) * 2^{327} + 1 is prime
repeat(327,71) * 2^{327} + 1 is prime
 328
repeat(328,4) + 1 is prime
repeat(328,12) + 1 is prime
repeat(328,14) * 2^{328}  328 + 1 is prime
repeat(328,36) * 2^{328} + 1 is prime
repeat(328,40) * 2^{328} + 1 is prime
repeat(328,45) * 2^{328}  328  1 is prime
repeat(328,56) * 2^{328}  2^{328} + 1 is prime
repeat(328,59) * 2^{328}  1 is prime
repeat(328,104) * 2^{328} + 2^{328}  1 is prime
repeat(328,108) * 2^{328}  1 is prime
repeat(328,116) * 2^{328} + 2^{328}  1 is prime
repeat(328,255) * 2^{328} + 1 is prime
repeat(328,324) * 2^{328} + 1 is prime
repeat(328,328) * 2^{328}  2^{328}  1 is prime
 329
repeat(329,13) * 2^{329} + 1 is prime
repeat(329,86) * 2^{329}  2^{329} + 1 is prime
repeat(329,90) * 2^{329}  2^{329} + 1 is prime
repeat(329,138) * 2^{329}  2^{329} + 1 is prime
repeat(329,139) * 2^{329} + 1 is prime
repeat(329,190) * 2^{329} + 1 is prime
 330
repeat(330,1) + 1 is prime
repeat(330,2) + 1 is prime
repeat(330,4) * 2^{330} + 1 is prime
repeat(330,8) + 1 is prime
repeat(330,12) * 2^{330}  330  1 is prime
repeat(330,14) + 1 is prime
repeat(330,17) + 1 is prime
repeat(330,18) * 2^{330}  330  1 is prime
repeat(330,28) * 2^{330}  330  1 is prime
repeat(330,30) * 2^{330} + 1 is prime
repeat(330,46) + 1 is prime
repeat(330,48) * 2^{330}  330  1 is prime
repeat(330,110) * 2^{330}  1 is prime
repeat(330,133) * 2^{330}  330 + 1 is prime
repeat(330,140) * 2^{330} + 1 is prime
repeat(330,162) * 2^{330} + 330 + 1 is prime
repeat(330,179) * 2^{330}  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) * 2^{332} + 2^{332} + 1 is prime
repeat(332,18) * 2^{332} + 2^{332} + 1 is prime
repeat(332,62) * 2^{332} + 1 is prime
repeat(332,68) + 1 is prime
repeat(332,106) * 2^{332}  2^{332} + 1 is prime
repeat(332,141) * 2^{332}  1 is prime
repeat(332,153) * 2^{332} + 2^{332} + 1 is prime
repeat(332,220) * 2^{332}  332  1 is prime
repeat(332,273) * 2^{332} + 1 is prime
repeat(332,300) * 2^{332}  1 is prime
 334
334*2^{334} + 334 + 2^{334}  1 is prime
 335
repeat(335,3) * 2^{335} + 2^{335}  1 is prime
repeat(335,61) * 2^{335} + 1 is prime
repeat(335,160) * 2^{335} + 1 is prime
repeat(335,216) * 2^{335}  2^{335} + 1 is prime
 336
repeat(336,1) + 1 is prime
repeat(336,2) * 2^{336} + 336 + 1 is prime
repeat(336,4) + 1 is prime
repeat(336,7) + 1 is prime
repeat(336,13) * 2^{336}  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) * 2^{336} + 2^{336} + 1 is prime
repeat(336,46) * 2^{336} + 336  1 is prime
repeat(336,65) + 1 is prime
repeat(336,94) + 1 is prime
repeat(336,210) * 2^{336} + 336 + 1 is prime
repeat(336,232) * 2^{336}  336 + 1 is prime
repeat(336,316) * 2^{336} + 2^{336} + 1 is prime
repeat(336,325) * 2^{336}  336  1 is prime
 339
repeat(339,12) * 2^{339}  1 is prime
repeat(339,92) * 2^{339} + 1 is prime
repeat(339,201) * 2^{339}  1 is prime
repeat(339,281) * 2^{339}  1 is prime
repeat(339,339) * 2^{339}  1 is prime
 342
repeat(342,2) + 1 is prime
repeat(342,28) + 1 is prime
repeat(342,32) * 2^{342} + 1 is prime
repeat(342,35) * 2^{342} + 2^{342} + 1 is prime
repeat(342,38) + 1 is prime
repeat(342,41) * 2^{342}  2^{342}  1 is prime
repeat(342,42) * 2^{342}  1 is prime
repeat(342,70) * 2^{342}  1 is prime
repeat(342,83) * 2^{342}  1 is prime
repeat(342,103) * 2^{342}  1 is prime
repeat(342,151) * 2^{342} + 342 + 1 is prime
repeat(342,168) * 2^{342} + 1 is prime
repeat(342,195) * 2^{342} + 2^{342} + 1 is prime
repeat(342,203) * 2^{342}  2^{342}  1 is prime
repeat(342,288) * 2^{342} + 1 is prime
 345
345*2^{345}  345  2^{345} is prime
 346
repeat(346,1) + 1 is prime
repeat(346,12) + 1 is prime
repeat(346,43) * 2^{346}  2^{346}  1 is prime
repeat(346,50) * 2^{346}  1 is prime
repeat(346,52) * 2^{346}  2^{346} + 1 is prime
repeat(346,53) * 2^{346} + 346 + 1 is prime
repeat(346,57) * 2^{346}  346  1 is prime
repeat(346,78) * 2^{346} + 346 + 1 is prime
repeat(346,129) + 1 is prime
repeat(346,141) * 2^{346}  2^{346}  1 is prime
repeat(346,143) * 2^{346}  346 + 1 is prime
repeat(346,148) * 2^{346}  2^{346} + 1 is prime
repeat(346,170) * 2^{346}  1 is prime
repeat(346,223) + 1 is prime
repeat(346,230) * 2^{346} + 346 + 1 is prime
repeat(346,238) * 2^{346}  346 + 1 is prime
repeat(346,240) * 2^{346}  346  1 is prime
repeat(346,287) * 2^{346} + 346  1 is prime
 348
repeat(348,1) + 1 is prime
repeat(348,10) * 2^{348}  1 is prime
repeat(348,18) * 2^{348}  348  1 is prime
repeat(348,31) * 2^{348}  1 is prime
repeat(348,59) * 2^{348}  2^{348}  1 is prime
repeat(348,137) * 2^{348}  1 is prime
repeat(348,189) + 1 is prime
repeat(348,254) * 2^{348}  348 + 1 is prime
repeat(348,330) * 2^{348}  348  1 is prime
 349
repeat(349,1) is prime
repeat(349,9) * 2^{349}  1 is prime
repeat(349,21) * 2^{349}  2^{349} + 1 is prime
repeat(349,58) * 2^{349}  1 is prime
repeat(349,60) * 2^{349} + 1 is prime
repeat(349,88) * 2^{349}  2^{349} + 1 is prime
repeat(349,111) * 2^{349}  1 is prime
repeat(349,286) * 2^{349}  1 is prime
 350
repeat(350,2) + 1 is prime
repeat(350,16) * 2^{350}  350 + 1 is prime
repeat(350,32) * 2^{350} + 1 is prime
repeat(350,38) * 2^{350} + 1 is prime
repeat(350,73) * 2^{350}  1 is prime
repeat(350,78) * 2^{350}  1 is prime
repeat(350,160) * 2^{350}  350 + 1 is prime
repeat(350,166) * 2^{350}  1 is prime
repeat(350,265) * 2^{350}  350  1 is prime
repeat(350,291) * 2^{350} + 350  1 is prime
 351
repeat(351,10) * 2^{351} + 1 is prime
repeat(351,204) * 2^{351} + 1 is prime
repeat(351,326) * 2^{351} + 1 is prime
 352
repeat(352,1) + 1 is prime
repeat(352,2) * 2^{352} + 2^{352} + 1 is prime
repeat(352,4) * 2^{352} + 2^{352}  1 is prime
repeat(352,5) * 2^{352}  2^{352} + 1 is prime
repeat(352,5) * 2^{352} + 2^{352}  1 is prime
repeat(352,7) + 1 is prime
repeat(352,39) + 1 is prime
repeat(352,114) + 1 is prime
repeat(352,173) * 2^{352}  2^{352} + 1 is prime
repeat(352,242) * 2^{352}  1 is prime
repeat(352,264) * 2^{352} + 2^{352} + 1 is prime
repeat(352,316) * 2^{352}  2^{352} + 1 is prime
repeat(352,336) * 2^{352} + 1 is prime
 354
repeat(354,14) * 2^{354}  354  1 is prime
repeat(354,18) * 2^{354} + 1 is prime
repeat(354,35) * 2^{354}  2^{354}  1 is prime
repeat(354,42) * 2^{354} + 1 is prime
repeat(354,46) * 2^{354} + 1 is prime
repeat(354,65) * 2^{354} + 354 + 1 is prime
repeat(354,109) * 2^{354}  354 + 1 is prime
repeat(354,117) * 2^{354}  2^{354}  1 is prime
repeat(354,122) * 2^{354} + 1 is prime
repeat(354,139) * 2^{354} + 2^{354} + 1 is prime
repeat(354,144) * 2^{354} + 354 + 1 is prime
repeat(354,220) * 2^{354}  354 + 1 is prime
repeat(354,289) * 2^{354} + 354 + 1 is prime
 356
repeat(356,18) + 1 is prime
repeat(356,20) + 1 is prime
repeat(356,35) * 2^{356}  2^{356}  1 is prime
repeat(356,42) * 2^{356} + 2^{356} + 1 is prime
repeat(356,129) * 2^{356}  2^{356}  1 is prime
repeat(356,178) * 2^{356} + 2^{356} + 1 is prime
repeat(356,218) * 2^{356}  2^{356} + 1 is prime
repeat(356,280) * 2^{356} + 2^{356} + 1 is prime
repeat(356,323) * 2^{356} + 356 + 1 is prime
repeat(356,348) * 2^{356} + 1 is prime
 357
repeat(357,8) * 2^{357}  1 is prime
repeat(357,26) * 2^{357}  1 is prime
repeat(357,35) * 2^{357}  1 is prime
repeat(357,105) * 2^{357}  1 is prime
repeat(357,197) * 2^{357}  1 is prime
repeat(357,232) * 2^{357}  1 is prime
 358
repeat(358,1) + 1 is prime
repeat(358,12) + 1 is prime
repeat(358,19) * 2^{358} + 1 is prime
repeat(358,34) * 2^{358}  2^{358} + 1 is prime
repeat(358,58) * 2^{358}  2^{358} + 1 is prime
repeat(358,96) * 2^{358} + 358 + 1 is prime
repeat(358,112) * 2^{358} + 1 is prime
repeat(358,155) * 2^{358}  2^{358} + 1 is prime
repeat(358,303) + 1 is prime
 360
repeat(360,3) + 1 is prime
repeat(360,4) * 2^{360} + 360  1 is prime
repeat(360,6) + 1 is prime
repeat(360,7) * 2^{360}  360 + 1 is prime
repeat(360,11) + 1 is prime
repeat(360,17) + 1 is prime
repeat(360,28) * 2^{360} + 360 + 1 is prime
repeat(360,44) + 1 is prime
repeat(360,48) * 2^{360} + 1 is prime
repeat(360,76) + 1 is prime
repeat(360,87) * 2^{360}  360  1 is prime
repeat(360,99) * 2^{360}  2^{360}  1 is prime
repeat(360,136) * 2^{360}  2^{360}  1 is prime
repeat(360,146) * 2^{360} + 1 is prime
repeat(360,152) * 2^{360}  360  1 is prime
repeat(360,154) * 2^{360}  2^{360}  1 is prime
repeat(360,185) * 2^{360}  1 is prime
repeat(360,194) * 2^{360} + 360 + 1 is prime
repeat(360,274) * 2^{360} + 1 is prime
repeat(360,297) + 1 is prime
repeat(360,360) * 2^{360} + 360  1 is prime
 361
repeat(361,12) * 2^{361}  2^{361} + 1 is prime
repeat(361,63) * 2^{361} + 1 is prime
repeat(361,66) * 2^{361} + 1 is prime
 362
362*2^{362}  1 is prime
 364
repeat(364,16) * 2^{364}  2^{364} + 1 is prime
repeat(364,29) * 2^{364}  364 + 1 is prime
repeat(364,37) * 2^{364}  2^{364}  1 is prime
repeat(364,114) * 2^{364} + 364 + 1 is prime
repeat(364,145) * 2^{364}  364  1 is prime
repeat(364,271) * 2^{364}  364 + 1 is prime
repeat(364,350) * 2^{364} + 364 + 1 is prime
 365
repeat(365,42) * 2^{365} + 2^{365}  1 is prime
repeat(365,246) * 2^{365}  1 is prime
 366
repeat(366,1) + 1 is prime
repeat(366,7) + 1 is prime
repeat(366,7) * 2^{366}  366  1 is prime
repeat(366,8) * 2^{366}  366  1 is prime
repeat(366,11) + 1 is prime
repeat(366,11) * 2^{366} + 2^{366} + 1 is prime
repeat(366,17) + 1 is prime
repeat(366,18) * 2^{366}  1 is prime
repeat(366,32) + 1 is prime
repeat(366,33) + 1 is prime
repeat(366,35) * 2^{366} + 366 + 1 is prime
repeat(366,37) + 1 is prime
repeat(366,46) * 2^{366}  1 is prime
repeat(366,50) * 2^{366}  366 + 1 is prime
repeat(366,55) * 2^{366} + 2^{366} + 1 is prime
repeat(366,109) + 1 is prime
repeat(366,116) * 2^{366}  366 + 1 is prime
repeat(366,139) * 2^{366} + 366  1 is prime
repeat(366,195) * 2^{366}  1 is prime
repeat(366,281) * 2^{366}  366  1 is prime
repeat(366,297) + 1 is prime
repeat(366,320) * 2^{366}  366  1 is prime
 365
repeat(365,42) * 2^{365} + 2^{365}  1 is prime
repeat(365,246) * 2^{365}  1 is prime
 366
repeat(366,1) + 1 is prime
repeat(366,7) + 1 is prime
repeat(366,7) * 2^{366}  366  1 is prime
repeat(366,8) * 2^{366}  366  1 is prime
repeat(366,11) + 1 is prime
repeat(366,11) * 2^{366} + 2^{366} + 1 is prime
repeat(366,17) + 1 is prime
repeat(366,18) * 2^{366}  1 is prime
repeat(366,32) + 1 is prime
repeat(366,33) + 1 is prime
repeat(366,35) * 2^{366} + 366 + 1 is prime
repeat(366,37) + 1 is prime
repeat(366,46) * 2^{366}  1 is prime
repeat(366,50) * 2^{366}  366 + 1 is prime
repeat(366,55) * 2^{366} + 2^{366} + 1 is prime
repeat(366,109) + 1 is prime
repeat(366,116) * 2^{366}  366 + 1 is prime
repeat(366,139) * 2^{366} + 366  1 is prime
repeat(366,195) * 2^{366}  1 is prime
repeat(366,281) * 2^{366}  366  1 is prime
repeat(366,297) + 1 is prime
repeat(366,320) * 2^{366}  366  1 is prime
 367
repeat(367,1) is prime
repeat(367,6) * 2^{367} + 1 is prime
repeat(367,10) * 2^{367}  2^{367}  1 is prime
repeat(367,244) * 2^{367}  2^{367}  1 is prime
repeat(367,284) * 2^{367} + 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) * 2^{368}  368  1 is prime
repeat(368,14) * 2^{368}  2^{368} + 1 is prime
repeat(368,15) + 1 is prime
repeat(368,19) * 2^{368}  368  1 is prime
repeat(368,24) + 1 is prime
repeat(368,42) + 1 is prime
repeat(368,49) * 2^{368} + 2^{368}  1 is prime
repeat(368,121) * 2^{368}  1 is prime
repeat(368,137) + 1 is prime
repeat(368,172) * 2^{368}  1 is prime
repeat(368,284) * 2^{368} + 1 is prime
repeat(368,344) * 2^{368} + 368 + 1 is prime
repeat(368,344) * 2^{368}  2^{368} + 1 is prime
 369
repeat(369,13) * 2^{369}  1 is prime
repeat(369,21) * 2^{369}  1 is prime
repeat(369,56) * 2^{369}  1 is prime
repeat(369,115) * 2^{369} + 2^{369}  1 is prime
repeat(369,362) * 2^{369}  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) * 2^{372}  372 + 1 is prime
repeat(372,18) * 2^{372} + 1 is prime
repeat(372,20) * 2^{372}  372  1 is prime
repeat(372,67) * 2^{372} + 1 is prime
repeat(372,100) + 1 is prime
repeat(372,126) * 2^{372}  1 is prime
repeat(372,137) * 2^{372}  372 + 1 is prime
repeat(372,148) * 2^{372}  1 is prime
repeat(372,340) + 1 is prime
 374
repeat(374,8) * 2^{374} + 374 + 1 is prime
repeat(374,14) * 2^{374}  374  1 is prime
repeat(374,18) * 2^{374} + 2^{374} + 1 is prime
repeat(374,25) * 2^{374}  374  1 is prime
repeat(374,37) * 2^{374}  374 + 1 is prime
repeat(374,37) * 2^{374} + 2^{374}  1 is prime
repeat(374,47) * 2^{374} + 1 is prime
repeat(374,47) * 2^{374}  2^{374} + 1 is prime
repeat(374,62) * 2^{374} + 1 is prime
repeat(374,82) * 2^{374}  374  1 is prime
repeat(374,107) * 2^{374} + 1 is prime
repeat(374,137) * 2^{374}  2^{374} + 1 is prime
repeat(374,177) * 2^{374}  374 + 1 is prime
repeat(374,205) * 2^{374}  374 + 1 is prime
repeat(374,283) * 2^{374}  374  1 is prime
repeat(374,340) * 2^{374}  374 + 1 is prime
 385
repeat(385,75) * 2^{385} + 1 is prime
repeat(385,96) * 2^{385}  1 is prime
repeat(385,228) * 2^{385}  2^{385} + 1 is prime
 377
repeat(377,9) * 2^{377}  1 is prime
repeat(377,95) * 2^{377}  1 is prime
repeat(377,182) * 2^{377}  1 is prime
repeat(377,273) * 2^{377}  1 is prime
 378
repeat(378,1) + 1 is prime
repeat(378,2) + 1 is prime
repeat(378,2) * 2^{378} + 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) * 2^{378}  1 is prime
repeat(378,25) + 1 is prime
repeat(378,33) * 2^{378} + 2^{378} + 1 is prime
repeat(378,53) * 2^{378} + 2^{378} + 1 is prime
repeat(378,55) + 1 is prime
repeat(378,64) + 1 is prime
repeat(378,70) * 2^{378}  378  1 is prime
repeat(378,87) * 2^{378} + 378 + 1 is prime
repeat(378,114) * 2^{378}  1 is prime
repeat(378,203) * 2^{378} + 2^{378} + 1 is prime
repeat(378,246) * 2^{378}  378  1 is prime
repeat(378,273) * 2^{378}  378  1 is prime
repeat(378,330) * 2^{378}  378  1 is prime
 380
repeat(380,8) + 1 is prime
repeat(380,35) * 2^{380} + 380 + 1 is prime
repeat(380,38) + 1 is prime
repeat(380,62) * 2^{380}  380  1 is prime
repeat(380,66) * 2^{380}  1 is prime
repeat(380,72) + 1 is prime
repeat(380,245) * 2^{380}  2^{380}  1 is prime
repeat(380,323) * 2^{380} + 1 is prime
 381
repeat(381,19) * 2^{381} + 2^{381}  1 is prime
repeat(381,29) * 2^{381} + 1 is prime
repeat(381,30) * 2^{381} + 1 is prime
repeat(381,31) * 2^{381} + 2^{381}  1 is prime
 382
repeat(382,1) + 1 is prime
repeat(382,26) * 2^{382}  1 is prime
repeat(382,39) + 1 is prime
repeat(382,54) * 2^{382}  2^{382}  1 is prime
repeat(382,74) * 2^{382} + 382  1 is prime
repeat(382,100) * 2^{382} + 382  1 is prime
repeat(382,101) * 2^{382} + 2^{382}  1 is prime
repeat(382,103) * 2^{382}  382 + 1 is prime
repeat(382,108) * 2^{382} + 2^{382} + 1 is prime
repeat(382,126) * 2^{382}  2^{382}  1 is prime
repeat(382,170) * 2^{382}  382 + 1 is prime
repeat(382,202) * 2^{382}  2^{382}  1 is prime
repeat(382,246) + 1 is prime
repeat(382,301) * 2^{382} + 382  1 is prime
 384
repeat(384,1) * 2^{384}  1 is prime
384*2^{384}  1 is prime
repeat(384,22) * 2^{384}  384 + 1 is prime
repeat(384,27) * 2^{384}  384 + 1 is prime
repeat(384,47) * 2^{384}  1 is prime
repeat(384,79) * 2^{384} + 2^{384} + 1 is prime
repeat(384,82) * 2^{384}  384 + 1 is prime
repeat(384,87) * 2^{384} + 384 + 1 is prime
repeat(384,177) * 2^{384}  1 is prime
repeat(384,198) * 2^{384} + 2^{384} + 1 is prime
repeat(384,215) * 2^{384}  1 is prime
repeat(384,367) * 2^{384} + 384 + 1 is prime
 385
repeat(385,75) * 2^{385} + 1 is prime
repeat(385,96) * 2^{385}  1 is prime
repeat(385,228) * 2^{385}  2^{385} + 1 is prime
 386
repeat(386,11) + 1 is prime
repeat(386,13) * 2^{386}  386 + 1 is prime
repeat(386,20) + 1 is prime
repeat(386,21) + 1 is prime
repeat(386,28) * 2^{386}  2^{386} + 1 is prime
repeat(386,41) + 1 is prime
repeat(386,48) * 2^{386}  1 is prime
repeat(386,55) * 2^{386} + 2^{386} + 1 is prime
repeat(386,63) * 2^{386} + 386  1 is prime
repeat(386,137) * 2^{386}  2^{386}  1 is prime
repeat(386,215) * 2^{386}  2^{386}  1 is prime
repeat(386,231) * 2^{386} + 386  1 is prime
repeat(386,295) * 2^{386}  2^{386} + 1 is prime
repeat(386,320) * 2^{386} + 386 + 1 is prime
 387
repeat(387,13) * 2^{387} + 1 is prime
repeat(387,61) * 2^{387}  2^{387} + 1 is prime
repeat(387,99) * 2^{387} + 2^{387}  1 is prime
repeat(387,234) * 2^{387} + 1 is prime
repeat(387,339) * 2^{387}  2^{387} + 1 is prime
 388
repeat(388,1) + 1 is prime
repeat(388,12) * 2^{388}  2^{388}  1 is prime
repeat(388,18) * 2^{388} + 388 + 1 is prime
repeat(388,33) + 1 is prime
repeat(388,37) * 2^{388}  2^{388}  1 is prime
repeat(388,40) + 1 is prime
repeat(388,53) * 2^{388}  2^{388} + 1 is prime
repeat(388,61) * 2^{388}  388 + 1 is prime
repeat(388,102) * 2^{388} + 388 + 1 is prime
repeat(388,103) * 2^{388}  388  1 is prime
repeat(388,207) * 2^{388}  388  1 is prime
repeat(388,224) * 2^{388} + 388 + 1 is prime
repeat(388,236) * 2^{388}  2^{388} + 1 is prime
repeat(388,273) * 2^{388}  1 is prime
repeat(388,281) * 2^{388}  2^{388} + 1 is prime
 389
repeat(389,1) is prime
repeat(389,24) * 2^{389} + 2^{389}  1 is prime
repeat(389,60) * 2^{389} + 2^{389}  1 is prime
repeat(389,136) * 2^{389} + 2^{389}  1 is prime
repeat(389,340) * 2^{389} + 2^{389}  1 is prime
 390
repeat(390,2) + 1 is prime
repeat(390,6) * 2^{390} + 1 is prime
repeat(390,14) + 1 is prime
repeat(390,20) * 2^{390} + 390 + 1 is prime
repeat(390,24) * 2^{390}  390 + 1 is prime
repeat(390,34) * 2^{390} + 1 is prime
repeat(390,111) * 2^{390}  390  1 is prime
repeat(390,144) * 2^{390} + 390  1 is prime
repeat(390,171) * 2^{390}  1 is prime
repeat(390,231) + 1 is prime
repeat(390,231) * 2^{390} + 390  1 is prime
repeat(390,280) + 1 is prime
repeat(390,338) * 2^{390}  390  1 is prime
repeat(390,375) * 2^{390}  390 + 1 is prime
 391
repeat(391,16) * 2^{391} + 2^{391} + 1 is prime
repeat(391,50) * 2^{391}  2^{391}  1 is prime
repeat(391,204) * 2^{391}  1 is prime
repeat(391,364) * 2^{391}  1 is prime
 392
repeat(392,21) + 1 is prime
repeat(392,27) + 1 is prime
repeat(392,46) * 2^{392}  1 is prime
repeat(392,99) + 1 is prime
repeat(392,107) * 2^{392} + 392  1 is prime
repeat(392,166) * 2^{392}  1 is prime
 393
repeat(393,118) * 2^{393} + 1 is prime
repeat(393,155) * 2^{393} + 1 is prime
repeat(393,354) * 2^{393} + 1 is prime
 394
repeat(394,2) * 2^{394} + 2^{394}  1 is prime
repeat(394,12) * 2^{394} + 394 + 1 is prime
repeat(394,25) * 2^{394} + 394  1 is prime
repeat(394,74) * 2^{394}  394 + 1 is prime
repeat(394,264) * 2^{394}  394  1 is prime
repeat(394,369) * 2^{394}  2^{394}  1 is prime
repeat(394,371) * 2^{394} + 394  1 is prime
 395
repeat(395,18) * 2^{395}  2^{395} + 1 is prime
repeat(395,35) * 2^{395} + 2^{395} + 1 is prime
repeat(395,138) * 2^{395}  2^{395} + 1 is prime
repeat(395,318) * 2^{395}  2^{395} + 1 is prime
 396
396*2^{396}  396  2^{396}  1 is prime
 397
repeat(397,1) is prime
repeat(397,54) * 2^{397}  1 is prime
 398
repeat(398,9) * 2^{398} + 2^{398} + 1 is prime
repeat(398,120) * 2^{398} + 1 is prime
repeat(398,139) * 2^{398}  1 is prime
repeat(398,153) * 2^{398} + 2^{398} + 1 is prime
repeat(398,159) * 2^{398}  2^{398}  1 is prime
repeat(398,191) * 2^{398} + 398 + 1 is prime
repeat(398,222) * 2^{398} + 1 is prime
repeat(398,273) * 2^{398} + 2^{398} + 1 is prime
 412
412*2^{412} + 412 + 2^{412}  1 is prime
 423
423*2^{423}  423 + 2^{423} is prime
 426
426*2^{426} + 426 + 1 is prime
 439
439*2^{439} + 439 + 2^{439} is prime
 462
462*2^{462}  1 is prime
 478
478*2^{478}  478  1 is prime
 483
483*2^{483} + 483  2^{483} is prime
 500
500*2^{500}  500  2^{500}  1 is prime
 512
512*2^{512}  1 is prime
 563
563*2^{563} + 563  2^{563} is prime
 565
565*2^{565} + 565 + 2^{565} is prime
 574
574*2^{574}  574 + 1 is prime
 600
600*2^{600}  600 + 1 is prime
 604
604*2^{604}  604  1 is prime
 621
621*2^{621}  621  2^{621} is prime
 628
628*2^{628}  628 + 1 is prime
 634
634*2^{634}  634  1 is prime
 705
705*2^{705}  705  2^{705} is prime
 749
749*2^{749} + 749 + 2^{749} is prime
 790
790*2^{790}  790  1 is prime
 822
822*2^{822}  1 is prime
 844
844*2^{844}  844  2^{844}  1 is prime
 868
868*2^{868}  868  1 is prime
 902
902*2^{902} + 902 + 2^{902}  1 is prime
 987
978*2^{978} + 978 + 1 is prime
 1015
1015*2^{1015} + 1015  2^{1015} is prime
 1106
1106*2^{1106} + 1106 + 2^{1106}  1 is prime
 1120
1120*2^{1120} + 1120  1 is prime
 1264
1264*2^{1264}  1264  1 is prime
 1364
1364*2^{1364} + 1364 + 2^{1364}  1 is prime
 1376
1376*2^{1376}  1376  1 is prime
 1438
1438*2^{1438} + 1438  1 is prime
 1530
1530*2^{1530} + 1530 + 1 is prime
 1600
1600*2^{1600}  1600 + 1 is prime
 1613
1613^{2} = 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) < 10^{10}
1613 is the 17th prime in the prime sequence f(n)=4*n^{2}  4*n + 653
Note that f(0), f(1), ... , f(16), f(17), f(18) are all primes, while f(19) is not.
(760*10^{1613}  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 p1^{2} + p2^{3} ± 1 is a twin prime pair
82^{1613}  81^{1613} 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 2^{26}+1
π(1613) = 2^{8}1
π(1613) + 2*1619 is a perfect square of a prime
I.e., 59^{2}
 1630
1630*2^{1630} + 1630  2^{1630} + 1 is prime
 1637
1637*2^{1637} + 1637 + 2^{1637} is prime
 2161
2161*2^{2161} + 2161  2^{2161} is prime
 2192
2192*2^{2192} + 2192  2^{2192} + 1 is prime
 2339
2339*2^{2339} + 2339  2^{2339} is prime
 2536
2536*2^{2536}  2536  1 is prime
 2800
2800*2^{2800}  2800 + 1 is prime
 2812
2812*2^{2812} + 2812 + 2^{2812}  1 is prime
 2957
2957*2^{2957}  2957 + 2^{2957} is prime
 2974
2974*2^{2974} + 2974 + 2^{2974}  1 is prime
 3236
3236*2^{3236} + 3236 + 2^{3236}  1 is prime
 3370
3370*2^{3370} + 3370  1 is prime
 3396
3396*2^{3396}  3396 + 1 is prime
 3544
3544*2^{3544}  3544  1 is prime
 3696
3696*2^{3696}  3696  2^{3696}  1 is prime
 3913
3913*2^{3913} + 3913 + 2^{3913} is prime
 4736
4736*2^{4736} + 4736 + 2^{4736}  1 is prime
 4822
4822*2^{4822} + 4822 + 2^{4822}  1 is prime
 4885
4885*2^{4885}  4885  2^{4885} is prime
 5052
5052*2^{5052}  5052  2^{5052}  1 is prime
 5062
5062*2^{5062} + 5062  1 is prime
 5066
5066*2^{5066} + 5066  2^{5066} + 1 is prime
 5125
5125*2^{5125}  5125  2^{5125} is prime
 5268
5268*2^{5268} + 5268 + 1 is prime
 5312
5312*2^{5312}  1 is prime
 5328
5328*2^{5328}  5328  2^{5328}  1 is prime
 6300
6300*2^{6300}  6300  2^{6300}  1 is prime
 6322
6322*2^{6322} + 6322  2^{6322} + 1 is prime
 6564
6564*2^{6564}  6564  1 is prime
 6607
6607*2^{6607}  6607  2^{6607} is prime
 6714
6714*2^{6714} + 6714  1 is prime
 6790
6790*2^{6790} + 6790 + 2^{6790}  1 is prime
 6956
6956*2^{6956} + 6956  2^{6956} + 1 is prime
 7238
7238*2^{7238} + 7238 + 1 is prime
 7268
7268*2^{7268}  7268  1 is prime
 7328
7328*2^{7328} + 7328 + 2^{7328}  1 is prime
 7726
7726*2^{7726} + 7726 + 2^{7726}  1 is prime
 7780
7780*2^{7780}  7780  1 is prime
 7989
7989*2^{7989}  7989 + 2^{7989} is prime
 8366
8366*2^{8366}  8366  1 is prime
 8384
8384*2^{8384} + 8384 + 1 is prime
 8892
8892*2^{8892}  8892 + 1 is prime
 9426
9426*2^{9426}  9426 + 1 is prime
 9436
9436*2^{9436} + 9436  1 is prime
 9542
9542*2^{9542} + 9542 + 2^{9542}  1 is prime
 9605
9605*2^{9605} + 9605 + 2^{9605} is prime
 9696
9696*2^{9696} + 9696 + 1 is prime
 (37*10^{2883}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)/(10^{d}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^digcnt1);
}
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
