A156105 -id:A156105 - cp's OEIS frontend

A156104 Primes p such that p+36 is also prime.

5, 7, 11, 17, 23, 31, 37, 43, 47, 53, 61, 67, 71, 73, 101, 103, 113, 127, 131, 137, 157, 163, 191, 193, 197, 227, 233, 241, 257, 271, 277, 281, 311, 313, 317, 331, 337, 347, 353, 373, 383, 397, 421, 431, 443, 463, 467, 487, 521, 541, 557, 563, 571, 577, 607

Offset: 1

Vincenzo Librandi, Feb 08 2009

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

Cf. A156112.

Cf. sequences of the type p+n are primes: A001359 (n=2), A023200 (n=4), A023201 (n=6), A023202 (n=8), A023203 (n=10), A046133 (n=12), A153417 (n=14), A049488 (n=16), A153418 (n=18), A153419 (n=20), A242476 (n=22), A033560 (n=24), A252089 (n=26), A252090 (n=28), A049481 (n=30), A049489 (n=32), A252091 (n=34), this sequence (n=36); A062284 (n=50), A049490 (n=64), A156105 (n=72), A156107 (n=144).

[p: p in PrimesUpTo(1000) | IsPrime(p + 36)]; // Vincenzo Librandi, Oct 31 2012

Select[Prime[Range[1000]], PrimeQ[(#+ 36)]&] (* Vincenzo Librandi, Oct 31 2012 *)

A252089 Primes p such that p + 26 is prime.

Original entry on oeis.org

3, 5, 11, 17, 41, 47, 53, 71, 83, 101, 113, 131, 137, 167, 173, 197, 251, 257, 281, 311, 347, 353, 383, 431, 461, 521, 587, 593, 617, 647, 683, 701, 743, 761, 797, 827, 857, 881, 911, 941, 971, 983, 1013, 1061, 1091, 1097, 1103, 1187, 1223, 1277, 1301, 1373

Offset: 1

Vincenzo Librandi, Dec 14 2014

			17 is in this sequence because 17+26 = 43 is prime.
431 is in this sequence because 431+26 = 457 is prime.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. sequences of the type p+n are primes: A001359 (n=2), A023200 (n=4), A023201 (n=6), A023202 (n=8), A023203 (n=10), A046133 (n=12), A153417 (n=14), A049488 (n=16), A153418 (n=18), A153419 (n=20), A242476 (n=22), A033560 (n=24), this sequence (n=26), A252090 (n=28), A049481 (n=30), A049489 (n=32), A252091 (n=34), A156104 (n=36); A062284 (n=50), A049490 (n=64), A156105 (n=72), A156107 (n=144).

[NthPrime(n): n in [1..250] | IsPrime(NthPrime(n)+26)];

Select[Prime[Range[200]], PrimeQ[# + 26] &]

A156112 Primes p such that p+36 and p+72 are both prime.

Original entry on oeis.org

7, 11, 17, 31, 37, 67, 101, 127, 157, 191, 197, 241, 277, 281, 311, 317, 337, 347, 431, 521, 541, 571, 647, 751, 787, 911, 941, 947, 977, 997, 1051, 1151, 1187, 1451, 1487, 1621, 1627, 1877, 2017, 2027, 2237, 2311, 2467, 2521, 2621, 2647, 2657, 2677, 2731

Offset: 1

Vincenzo Librandi, Feb 08 2009

A156105 INTERSECT A156104. [R. J. Mathar, Feb 09 2009]

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

Cf. A156104, A156105.

[p: p in PrimesUpTo(3000)|IsPrime(p + 36) and IsPrime (p + 72)]; // Vincenzo Librandi, Oct 31 2012

Select[Prime[Range[3000]], And @@ PrimeQ[{# + 36,# + 72}]&] (* Vincenzo Librandi, Oct 31 2012 *)
Select[Prime[Range[3000]],AllTrue[#+{36,72},PrimeQ]&] (* Harvey P. Dale, Jul 12 2023 *)

More terms from R. J. Mathar, Feb 09 2009

A156124 Primes p, such that p+72 and p+144 are both prime.

Original entry on oeis.org

7, 29, 37, 67, 79, 107, 127, 139, 167, 239, 277, 317, 347, 359, 419, 449, 499, 547, 739, 809, 839, 919, 947, 1019, 1217, 1229, 1289, 1327, 1367, 1399, 1409, 1427, 1439, 1549, 1597, 1789, 1997, 2017, 2069, 2237, 2239, 2267, 2477, 2549, 2647, 2657, 2659, 2897

Offset: 1

Vincenzo Librandi, Feb 08 2009

A156105 INTERSECT A156107. [R. J. Mathar, Jul 13 2009]

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

Cf. A156105, A156107.

[p: p in PrimesUpTo(3000)|IsPrime(p + 72)and IsPrime (p + 144)]; // Vincenzo Librandi, Oct 31 2012

Select[Prime[Range[3000]], And @@ PrimeQ[{# + 72, # + 144}]&] (* Vincenzo Librandi, Oct 31 2012 *)

More terms from R. J. Mathar, Jul 13 2009

A156110 Primes p such that p+18 and p+72 are both prime.

Original entry on oeis.org

11, 29, 41, 79, 109, 139, 179, 211, 239, 349, 431, 449, 491, 569, 601, 701, 739, 751, 809, 811, 839, 911, 919, 991, 1021, 1031, 1051, 1091, 1231, 1289, 1301, 1381, 1409, 1471, 1481, 1549, 1759, 1861, 1931, 2011, 2069, 2081, 2221, 2269, 2339, 2459, 2521

Offset: 1

Vincenzo Librandi, Feb 08 2009

A153418 INTERSECT A156105. [Bruno Berselli, Nov 01 2012]

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

Cf. A153418, A156105.

[p: p in PrimesUpTo(3000)|IsPrime(p + 18) and IsPrime (p + 72)]; // Vincenzo Librandi, Oct 31 2012

Select[Prime[Range[3000]], And @@ PrimeQ[{# + 18, # + 72}]&] (* Vincenzo Librandi, Oct 31 2012 *)

A274045 Primes p such that p + 72 is the next prime.

Original entry on oeis.org

31397, 360091, 507217, 517639, 633667, 650107, 705317, 749471, 753859, 770669, 809629, 818021, 828277, 1001839, 1025957, 1087159, 1133387, 1145899, 1152421, 1164101, 1206869, 1207769, 1210639, 1241087, 1278911, 1290719, 1351997

Offset: 1

Karl V. Keller, Jr., Jun 07 2016

nonn

This sequence is a subsequence of A156105 (p and p + 72 are primes).

			For 31397, the next prime is 31397 + 72 = 31469.
For 360091, the next prime is 360091 + 72 = 360163.

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000

Cf. A000040, A204792.

Select[Partition[Prime[Range[105000]],2,1],#[[2]]-#[[1]]==72&][[All,1]] (* Harvey P. Dale, Dec 19 2021 *)

is(n)=isprime(n) && nextprime(n+1)-n==72 \\ Charles R Greathouse IV, Jun 19 2016

from sympy import isprime,nextprime
for i in range(3,1500001,2):
  if isprime(i) and nextprime(i) == i+72: print(i,end=', ')

cp's OEIS Frontend

A156104 Primes p such that p+36 is also prime.

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A252089 Primes p such that p + 26 is prime.

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A156112 Primes p such that p+36 and p+72 are both prime.

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A156124 Primes p, such that p+72 and p+144 are both prime.

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Magma

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Extensions

A156110 Primes p such that p+18 and p+72 are both prime.

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Magma

Mathematica

A274045 Primes p such that p + 72 is the next prime.

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Python