Repunit
List of repunit primes base b {\displaystyle b}
Smallest prime such that is prime are (start with, 0 if no such exists) 3, 3, 0, 3, 3, 5, 3, 0, 19, 17, 3, 5, 3, 3, 0, 3, 25667, 19, 3, 3, 5, 5, 3, 0, 7, 3, 5, 5, 5, 7, 0, 3, 13, 313, 0, 13, 3, 349, 5, 3, 1319, 5, 5, 19, 7, 127, 19, 0, 3, 4229, 103, 11, 3, 17, 7, 3, 41, 3, 7, 7, 3, 5, 0, 19, 3, 19, 5, 3, 29, 3, 7, 5, 5, 3, 41, 3, 3, 5, 3, 0, 23, 5, 17, 5, 11, 7, 61, 3, 3, 4421, 439, 7, 5, 7, 3343, 17, 13, 3, 0, ...

Repunit

Section Title: List of repunit primes base b {\displaystyle b}
Table Section Text: Smallest prime such that is prime are (start with, 0 if no such exists) 3, 3, 0, 3, 3, 5, 3, 0, 19, 17, 3, 5, 3, 3, 0, 3, 25667, 19, 3, 3, 5, 5, 3, 0, 7, 3, 5, 5, 5, 7, 0, 3, 13, 313, 0, 13, 3, 349, 5, 3, 1319, 5, 5, 19, 7, 127, 19, 0, 3, 4229, 103, 11, 3, 17, 7, 3, 41, 3, 7, 7, 3, 5, 0, 19, 3, 19, 5, 3, 29, 3, 7, 5, 5, 3, 41, 3, 3, 5, 3, 0, 23, 5, 17, 5, 11, 7, 61, 3, 3, 4421, 439, 7, 5, 7, 3343, 17, 13, 3, 0, ...

numbers such that is prime (some large terms are only corresponding to probable primes, these are checked up to 100000)	OEIS sequence

−50	1153, 26903, 56597, ...

−49	7, 19, 37, 83, 1481, 12527, 20149, ...	A237052

−48	2*, 5, 17, 131, 84589, ...	A236530

−47	5, 19, 23, 79, 1783, 7681, ...	A236167

−46	7, 23, 59, 71, 107, 223, 331, 2207, 6841, 94841, ...	A235683

−45	103, 157, 37159, ...

−44	2*, 7, 41233, ...

−43	5, 7, 19, 251, 277, 383, 503, 3019, 4517, 9967, 29573, ...	A231865

−42	2*, 3, 709, 1637, 17911, 127609, ...	A231604

−41	17, 691, 113749, ...

−40	53, 67, 1217, 5867, 6143, 11681, 29959, ...	A229663

−39	3, 13, 149, 15377, ...	A230036

−38	2*, 5, 167, 1063, 1597, 2749, 3373, 13691, 83891, 131591, ...	A229524

−37	5, 7, 2707, ...

−36	31, 191, 257, 367, 3061, 110503, ...	A229145

−35	11, 13, 79, 127, 503, 617, 709, 857, 1499, 3823, 135623, ...	A185240

−34	3, 294277, ...

−33	5, 67, 157, 12211, ...	A185230

−32	2* (no others)

−31	109, 461, 1061, 50777, ...	A126856

−30	2*, 139, 173, 547, 829, 2087, 2719, 3109, 10159, 56543, 80599, ...	A071382

−29	7, 112153, 151153, ...	A291906

−28	3, 19, 373, 419, 491, 1031, 83497, ...	A071381

−27	(none)

−26	11, 109, 227, 277, 347, 857, 2297, 9043, ...	A071380

−25	3, 7, 23, 29, 59, 1249, 1709, 1823, 1931, 3433, 8863, 43201, 78707, ...	A057191

−24	2*, 7, 11, 19, 2207, 2477, 4951, ...	A057190

−23	11, 13, 67, 109, 331, 587, 24071, 29881, 44053, ...	A057189

−22	3, 5, 13, 43, 79, 101, 107, 227, 353, 7393, 50287, ...	A057188

−21	3, 5, 7, 13, 37, 347, 17597, 59183, 80761, 210599, 394579, ...	A057187

−20	2*, 5, 79, 89, 709, 797, 1163, 6971, 140053, 177967, 393257, ...	A057186

−19	17, 37, 157, 163, 631, 7351, 26183, 30713, 41201, 77951, 476929, ...	A057185

−18	2*, 3, 7, 23, 73, 733, 941, 1097, 1933, 4651, 481147, ...	A057184

−17	7, 17, 23, 47, 967, 6653, 8297, 41221, 113621, 233689, 348259, ...	A057183

−16	3, 5, 7, 23, 37, 89, 149, 173, 251, 307, 317, 30197, 1025393, ...	A057182

−15	3, 7, 29, 1091, 2423, 54449, 67489, 551927, ...	A057181

−14	2*, 7, 53, 503, 1229, 22637, 1091401, ...	A057180

−13	3, 11, 17, 19, 919, 1151, 2791, 9323, 56333, 1199467, ...	A057179

−12	2*, 5, 11, 109, 193, 1483, 11353, 21419, 21911, 24071, 106859, 139739, 495953, ...	A057178

−11	5, 7, 179, 229, 439, 557, 6113, 223999, 327001, ...	A057177

−10	5, 7, 19, 31, 53, 67, 293, 641, 2137, 3011, 268207, ...	A001562

−9	3, 59, 223, 547, 773, 1009, 1823, 3803, 49223, 193247, 703393, ...	A057175

−8	2* (no others)

−7	3, 17, 23, 29, 47, 61, 1619, 18251, 106187, 201653, 1178033, ...	A057173

−6	2*, 3, 11, 31, 43, 47, 59, 107, 811, 2819, 4817, 9601, 33581, 38447, 41341, 131891, 196337, 1313371, ...	A057172

−5	5, 67, 101, 103, 229, 347, 4013, 23297, 30133, 177337, 193939, 266863, 277183, 335429, 1856147, ...	A057171

−4	2*, 3 (no others)

−3	2*, 3, 5, 7, 13, 23, 43, 281, 359, 487, 577, 1579, 1663, 1741, 3191, 9209, 11257, 12743, 13093, 17027, 26633, 104243, 134227, 152287, 700897, 1205459, ...	A007658

−2	3, 4*, 5, 7, 11, 13, 17, 19, 23, 31, 43, 61, 79, 101, 127, 167, 191, 199, 313, 347, 701, 1709, 2617, 3539, 5807, 10501, 10691, 11279, 12391, 14479, 42737, 83339, 95369, 117239, 127031, 138937, 141079, 267017, 269987, 374321, 986191, 4031399, ..., 13347311, 13372531, ...	A000978

2	2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609, ..., 57885161, ..., 74207281, ..., 77232917, ...	A000043

3	3, 7, 13, 71, 103, 541, 1091, 1367, 1627, 4177, 9011, 9551, 36913, 43063, 49681, 57917, 483611, 877843, 2215303, ...	A028491

4	2 (no others)

5	3, 7, 11, 13, 47, 127, 149, 181, 619, 929, 3407, 10949, 13241, 13873, 16519, 201359, 396413, 1888279, ...	A004061

6	2, 3, 7, 29, 71, 127, 271, 509, 1049, 6389, 6883, 10613, 19889, 79987, 608099, ...	A004062

7	5, 13, 131, 149, 1699, 14221, 35201, 126037, 371669, 1264699, ...	A004063

8	3 (no others)

9	(none)

10	2, 19, 23, 317, 1031, 49081, 86453, 109297, 270343, ...	A004023

11	17, 19, 73, 139, 907, 1907, 2029, 4801, 5153, 10867, 20161, 293831, ...	A005808

12	2, 3, 5, 19, 97, 109, 317, 353, 701, 9739, 14951, 37573, 46889, 769543, ...	A004064

13	5, 7, 137, 283, 883, 991, 1021, 1193, 3671, 18743, 31751, 101089, ...	A016054

14	3, 7, 19, 31, 41, 2687, 19697, 59693, 67421, 441697, ...	A006032

15	3, 43, 73, 487, 2579, 8741, 37441, 89009, 505117, 639833, ...	A006033

16	2 (no others)

17	3, 5, 7, 11, 47, 71, 419, 4799, 35149, 54919, 74509, ...	A006034

18	2, 25667, 28807, 142031, 157051, 180181, 414269, ...	A133857

19	19, 31, 47, 59, 61, 107, 337, 1061, 9511, 22051, 209359, ...	A006035

20	3, 11, 17, 1487, 31013, 48859, 61403, 472709, ...	A127995

21	3, 11, 17, 43, 271, 156217, 328129, ...	A127996

22	2, 5, 79, 101, 359, 857, 4463, 9029, 27823, ...	A127997

23	5, 3181, 61441, 91943, 121949, ...	A204940

24	3, 5, 19, 53, 71, 653, 661, 10343, 49307, 115597, 152783, ...	A127998

25	(none)

26	7, 43, 347, 12421, 12473, 26717, ...	A127999

27	3 (no others)

28	2, 5, 17, 457, 1423, 115877, ...	A128000

29	5, 151, 3719, 49211, 77237, ...	A181979

30	2, 5, 11, 163, 569, 1789, 8447, 72871, 78857, 82883, ...	A098438

31	7, 17, 31, 5581, 9973, 101111, ...	A128002

32	(none)

33	3, 197, 3581, 6871, 183661, ...	A209120

34	13, 1493, 5851, 6379, 125101, ...	A185073

35	313, 1297, ...

36	2 (no others)

37	13, 71, 181, 251, 463, 521, 7321, 36473, 48157, 87421, ...	A128003

38	3, 7, 401, 449, 109037, ...	A128004

39	349, 631, 4493, 16633, 36341, ...	A181987

40	2, 5, 7, 19, 23, 29, 541, 751, 1277, ...	A128005

41	3, 83, 269, 409, 1759, 11731, ...	A239637

42	2, 1319, ...

43	5, 13, 6277, 26777, 27299, 40031, 44773, ...	A240765

44	5, 31, 167, 100511, ...	A294722

45	19, 53, 167, 3319, 11257, 34351, ...	A242797

46	2, 7, 19, 67, 211, 433, 2437, 2719, 19531, ...	A243279

47	127, 18013, 39623, ...	A267375

48	19, 269, 349, 383, 1303, 15031, ...	A245237

49	(none)

50	3, 5, 127, 139, 347, 661, 2203, 6521, ...	A245442

Sentence(s)

The repunit is prime for n = 2, 19, 23, 317, 1031, ... is sequence of A004023 in OEIS.

final_sentence: The repunit is prime for n = 2, 19, 23, 317, 1031, ... is sequence of A004023 in OEIS.