A141977 -id:A141977 - cp's OEIS frontend

A142005 Primes congruent to 1 mod 31.

311, 373, 683, 1117, 1303, 1427, 1489, 1613, 1861, 2357, 2543, 2729, 2791, 3163, 3659, 3907, 4093, 4217, 4651, 5023, 5147, 5209, 5333, 5519, 5581, 5953, 6263, 6449, 6883, 7069, 7193, 7937, 8123, 8681, 8867, 8929, 9239, 9859, 10169, 10789, 11161, 11471, 11657

Offset: 1

N. J. A. Sloane, Jul 11 2008

Primes congruent to 1 mod 62. - Chai Wah Wu, Apr 28 2025

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A141977.

[p: p in PrimesUpTo(12000) | p mod 31 eq 1 ]; // Vincenzo Librandi, Aug 17 2012

Select[Range[1,20000,31],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 07 2011 *)

is(n)=isprime(n) && n%31==1 \\ Charles R Greathouse IV, Jul 01 2016

A142006 Primes congruent to 2 mod 31.

Original entry on oeis.org

2, 157, 281, 467, 653, 839, 1087, 1459, 1583, 1831, 2017, 2141, 2203, 2389, 2699, 3257, 3319, 3691, 3877, 4001, 4373, 4621, 4931, 4993, 5179, 5303, 5737, 5861, 5923, 6047, 6481, 6791, 6977, 7039, 7349, 7411, 7907, 8093, 8527, 8713, 8837, 9209, 9643, 9767

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A141977, A142005.

[p: p in PrimesUpTo(12000) | p mod 31 eq 2 ]; // Vincenzo Librandi, Aug 17 2012

Select[Range[2,20000,31],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 07 2011 *)

select(n->n%31==2, primes(1000)) \\ Charles R Greathouse IV, Apr 28 2015

{2} UNION A142874. - R. J. Mathar, Jul 20 2008

a(n) ~ 30n log n. - Charles R Greathouse IV, Apr 28 2015

A141978 Primes congruent to 2 mod 29.

Original entry on oeis.org

2, 31, 89, 263, 379, 727, 1249, 1307, 1423, 1481, 1597, 2003, 2293, 2351, 2467, 2699, 3163, 3221, 3511, 3917, 4091, 4729, 4787, 4903, 5077, 5309, 5483, 5657, 6121, 6353, 6469, 6701, 6991, 7687, 7919, 8093, 8209, 8731, 8963, 9137, 9311, 9601, 9833, 9949

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A141977.

[ p: p in PrimesUpTo(11000) | p mod 29 eq 2 ]; // Vincenzo Librandi, Apr 07 2011

Select[Range[2,20000,29],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 06 2011 *)

is(n)=isprime(n) && n%29==2 \\ Charles R Greathouse IV, Jul 01 2016

{2} UNION A142715. - R. J. Mathar, Jul 20 2008

A140444 Primes congruent to 1 (mod 14).

Original entry on oeis.org

29, 43, 71, 113, 127, 197, 211, 239, 281, 337, 379, 421, 449, 463, 491, 547, 617, 631, 659, 673, 701, 743, 757, 827, 883, 911, 953, 967, 1009, 1051, 1093, 1163, 1289, 1303, 1373, 1429, 1471, 1499, 1583, 1597, 1667, 1709, 1723, 1877, 1933, 2003, 2017, 2087

Offset: 1

Juri-Stepan Gerasimov, Jun 26 2008

From Federico Provvedi, May 24 2018: (Start)
Also primes congruent to 1 (mod 7).
For every prime p > 2, primes congruent to 1 (mod p) are also congruent to 1 (mod 2*p).
Conjecture: The monic polynomial P(x) = (x+1)^7/x - 1/x = ((x+1)^7-1)/x is irreducible but factorizable over Galois field (mod a(n)) with exactly 6 distinct irreducible factors of degree 1. Examples:
P(x) == (5 + x) (6 + x) (7 + x) (10 + x) (14 + x) (23 + x)    (mod 29)
P(x) == (3 + x) (9 + x) (23 + x) (28 + x) (33 + x) (40 + x)   (mod 43)
P(x) == (24 + x) (27 + x) (35 + x) (40 + x) (42 + x) (52 + x) (mod 71)
P(x) == (5 + x) (8 + x) (65 + x) (84 + x) (86 + x) (98 + x)   (mod 113)
... (End).
Primes in A131877. - Eric Chen, Jun 14 2018

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Jorma K. Merikoski, Pentti Haukkanen, and Timo Tossavainen, The congruence x^n = -a^n (mod m): Solvability and related OEIS sequences, Notes. Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 516-529. See p. 526.

Cf. A045437, A045458, A045471, A045473.
A090613 gives prime index.
Cf. A090614.
Cf. A131877.
Primes congruent to 1 (mod k): A000040 (k=1), A065091 (k=2), A002476 (k=3 and 6), A002144 (k=4), A030430 (k=5 and 10), this sequence (k=7 and 14), A007519 (k=8), A061237 (k=9 and 18), A141849 (k=11 and 22), A068228 (k=12), A268753 (k=13 and 26), A132230 (k=15 and 30), A094407 (k=16), A129484 (k=17 and 34), A141868 (k=19 and 38), A141881 (k=20), A124826 (k=21 and 42), A212374 (k=23 and 46), A107008 (k=24), A141927 (k=25 and 50), A141948 (k=27 and 54), A093359 (k=28), A141977 (k=29 and 58), A142005 (k=31 and 62), A133870 (k=32).

Filtered(Filtered([1..2300],n->n mod 14=1),IsPrime); # Muniru A Asiru, Jun 27 2018

[p: p in PrimesUpTo(3000)|p mod 14 in {1}]; // Vincenzo Librandi, Dec 18 2010

select(isprime,select(n->modp(n,14)=1,[$1..2300])); # Muniru A Asiru, Jun 27 2018

Select[Prime[Range[500]], Mod[#, 14] == 1 &]  (* Harvey P. Dale, Mar 21 2011 *)

is(n)=isprime(n) && n%14==1 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 6n log n. - Charles R Greathouse IV, Jul 02 2016

Simpler definition from N. J. A. Sloane, Jul 11 2008

A142003 Primes congruent to 27 mod 29.

Original entry on oeis.org

317, 433, 491, 607, 839, 1013, 1129, 1187, 1303, 1361, 1709, 1999, 2347, 2521, 2579, 2753, 2927, 3217, 3391, 3449, 3623, 3739, 3797, 4261, 4493, 4783, 4957, 5189, 5479, 5653, 5711, 5827, 6581, 6871, 7103, 7219, 7393, 7451, 7741, 8089, 8147, 8263, 8669

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A141977, A141978.

[p: p in PrimesUpTo(12000) | p mod 29 eq 27 ]; // Vincenzo Librandi, Aug 17 2012

Select[Range[27,20000,29],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 07 2011 *)

is(n)=isprime(n) && n%29==27 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 28n log n. - Charles R Greathouse IV, Jul 02 2016

A141979 Primes congruent to 3 mod 29.

Original entry on oeis.org

3, 61, 293, 409, 467, 641, 757, 1163, 1279, 1453, 1511, 1627, 1801, 2207, 2381, 2671, 2729, 2903, 3019, 3251, 3541, 3889, 3947, 4643, 4759, 4817, 4933, 5107, 5281, 5861, 6151, 6673, 7079, 7253, 7369, 7717, 7949, 8123, 8297, 8761, 8819, 9109, 9283, 9341

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A141977, A141978.

[ p: p in PrimesUpTo(11000) | p mod 29 eq 3 ]; // Vincenzo Librandi, Apr 07 2011

Select[Range[3,20000,29],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 06 2011 *)

is(n)=isprime(n) && n%29==3 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 28n log n. - Charles R Greathouse IV, Jul 02 2016

A141999 Primes congruent to 23 mod 29.

Original entry on oeis.org

23, 139, 197, 313, 487, 661, 719, 1009, 1531, 1879, 2053, 2111, 2459, 2633, 2749, 3271, 3329, 3677, 3793, 3851, 3967, 4373, 4547, 4663, 4721, 5011, 5417, 5591, 5881, 5939, 6113, 6229, 6287, 6577, 6983, 7331, 7621, 7853, 8317, 8839, 9013, 9187, 9419, 9767

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A141977, A141978.

[p: p in PrimesUpTo(12000) | p mod 29 eq 23 ]; // Vincenzo Librandi, Aug 17 2012

Select[Range[23,20000,29],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 07 2011 *)

is(n)=isprime(n) && n%29==23 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 28n log n. - Charles R Greathouse IV, Jul 02 2016

A142004 Primes congruent to 28 mod 29.

Original entry on oeis.org

173, 347, 463, 521, 811, 1217, 1913, 2029, 2087, 2203, 2377, 2551, 2609, 2957, 3769, 3943, 4001, 4349, 4523, 4639, 4813, 4871, 4987, 5393, 5683, 5741, 5857, 6089, 6263, 6379, 6553, 6959, 7307, 7481, 7829, 8293, 8467, 8641, 8699, 9221, 9337, 9511, 9743

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A141977, A141978.

[p: p in PrimesUpTo(12000) | p mod 29 eq 28 ]; // Vincenzo Librandi, Aug 17 2012

Select[Range[28,20000,29],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 07 2011 *)

is(n)=isprime(n) && n%29==28 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 28n log n. - Charles R Greathouse IV, Jul 02 2016

A248620 Lesser of twin primes of (29n + 1, 29n + 3).

Original entry on oeis.org

59, 1277, 1451, 3539, 4931, 5279, 9281, 9629, 10499, 11717, 12239, 16067, 22157, 23027, 23201, 24419, 26681, 31727, 34511, 35729, 37991, 40427, 45821, 47387, 48779, 55217, 59219, 60089, 70181, 70877, 72269, 75401, 77489, 79229, 80447, 83231, 85667, 88799

Offset: 1

Karl V. Keller, Jr., Oct 10 2014

nonn

Lesser of twin primes where A195819(n) + 1 and A195819(n) + 3 are both primes.

Intersection of A001359 and A141977.

			29 * 2 + 1 = 59, which is prime, and 61 is also prime, so 59 is in the sequence.
29 * 44 + 1 = 1277, which is prime, and 1279 is also prime, so 1277 is in the sequence.
29 * 50 + 1 = 1451, which is prime, and 1453 is also prime, so 1451 is in the sequence.
29 * 54 + 1 = 1567, which is prime, but 1569 = 3 * 523, so 1567 is not in the sequence.

Karl V. Keller, Jr., Table of n, a(n) for n = 1..1000

Cf. A001359 (Lesser of twin primes), A195819 (Multiples of 29).

Cf. A141977 (Primes congruent to 1 mod 29), A141979 (Primes congruent to 3 mod 29).

Select[58Range[1500] + 1, PrimeQ[#] && PrimeQ[# + 2] &] (* Alonso del Arte, Oct 31 2014 *)
Select[29*Range[2,3150,2],AllTrue[#+{1,3},PrimeQ]&]+1 (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 16 2019 *)

lista(nn) = {forstep (n=2, nn, 2, if (isprime(p=29*n+1) && isprime(29*n+3), print1(p, ", ")););} \\ Michel Marcus, Oct 17 2014

from math import *
from sympy import isprime
for n in range(0,10001):
  if isprime(58*n+1) and isprime(58*n+3): print (58*n+1,end=', ')

A141980 Primes congruent to 4 mod 29.

Original entry on oeis.org

149, 439, 613, 787, 1019, 1193, 1367, 1483, 1657, 1831, 1889, 2063, 2179, 2237, 2411, 3049, 3571, 3803, 3919, 4093, 4441, 4673, 4789, 5021, 5659, 5717, 6007, 6529, 6703, 6761, 7109, 7283, 7457, 7573, 8269, 8443, 8501, 8849, 9371, 9661, 9719, 10009, 10067

Offset: 1

N. J. A. Sloane, Jul 11 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A141977, A141978.

[ p: p in PrimesUpTo(11000) | p mod 29 eq 4 ]; // Vincenzo Librandi, Apr 07 2011

Select[Range[4,10000,29],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 06 2011 *)
Select[Prime[Range[1500]],Mod[#,29]==4&] (* Harvey P. Dale, Dec 24 2022 *)

is(n)=isprime(n) && n%29==4 \\ Charles R Greathouse IV, Jul 03 2016

a(n) ~ 28n log n. - Charles R Greathouse IV, Jul 03 2016

cp's OEIS Frontend

A142005 Primes congruent to 1 mod 31.

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A142006 Primes congruent to 2 mod 31.

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A141978 Primes congruent to 2 mod 29.

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A140444 Primes congruent to 1 (mod 14).

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A142003 Primes congruent to 27 mod 29.

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Magma

Mathematica

PARI

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A141979 Primes congruent to 3 mod 29.

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Magma

Mathematica

PARI

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A141999 Primes congruent to 23 mod 29.

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Magma

Mathematica