A153507 -id:A153507 - cp's OEIS frontend

A174363 Primes p such that 2*p^3 -+ 3 are also prime.

2, 13, 1223, 2357, 4013, 4027, 4507, 5903, 8713, 9623, 10663, 11717, 12757, 12983, 13883, 15877, 16103, 16787, 16823, 16883, 18097, 22697, 23357, 24677, 26107, 27953, 28603, 30313, 31327, 34147, 35617, 35933, 41183, 44893, 46687, 46817, 48247, 50417, 52963, 54083

Offset: 1

Vincenzo Librandi, Mar 17 2010

nonn

Intersection of A153507 and A243630. - Felix Fröhlich, Nov 27 2019

			For p=2, 2*2^3 -+ 3 = (13, 19), both prime, so 2 is a term of the sequence.
For p=13, 2*13^3 -+ 3 = (4391, 4397), both prime, so 13 is a term of the sequence.

Harvey P. Dale and K. D. Bajpai, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Cf. A153507, A243630.

[p: p in PrimesUpTo(100000)|IsPrime(2*p^3-3) and IsPrime(2*p^3+3)]

select(p -> andmap(isprime, [p, 2*p^3+3, 2*p^3-3]), [seq(p, p=1.. 10^5)]); # K. D. Bajpai, Nov 28 2019

Select[Prime[Range[5000]],And@@PrimeQ[2 #^3+{3,-3}]&] (* Harvey P. Dale, Jan 25 2013 *)

forprime(p=1, 55000, if(ispseudoprime(2*p^3-3) && ispseudoprime(2*p^3+3), print1(p, ", "))) \\ Felix Fröhlich, Nov 27 2019

A243595 Primes p such that 3 + 2*p^2 is also prime.

Original entry on oeis.org

2, 5, 7, 23, 37, 43, 47, 83, 103, 107, 113, 127, 197, 373, 433, 463, 467, 523, 547, 587, 593, 617, 733, 743, 797, 863, 877, 887, 953, 1097, 1163, 1213, 1297, 1427, 1493, 1567, 1583, 1657, 1667, 1693, 1783, 1877, 1987, 2053, 2063, 2087, 2207, 2357, 2557, 2753

Offset: 1

Zak Seidov, Jun 07 2014

Corresponding primes 3 + 2*p^2 are congruent to 5 modulo 6.

			2 is in the sequence because 3+2*2^2 = 11 is prime; also, for the comment, 11 = 6+5.
5 is in the sequence because 3+2*5^2 = 53 is prime, also 53 = 6*8+5.
7 is in the sequence because 3+2*7^2 = 101 is prime, also 101 = 6*16+5.

Bruno Berselli, Table of n, a(n) for n = 1..1000

Cf. A002476, A033203, A153507, A161724.

[p: p in PrimesUpTo(4000) | IsPrime(3+2*p^2)]; // Bruno Berselli, Jun 07 2014

Select[Prime[Range[500]], PrimeQ[3 + 2 #^2] &] (* Bruno Berselli, Jun 07 2014 *)

s=[]; forprime(p=2, 4000, if(isprime(3+2*p^2), s=concat(s, p))); s \\ Colin Barker, Jun 07 2014

[p for p in primes(4000) if is_prime(3+2*p^2)] # Bruno Berselli, Jun 07 2014

A243630 Primes p such that 2*p^3 - 3 is also prime.

Original entry on oeis.org

2, 7, 11, 13, 47, 101, 107, 151, 163, 167, 251, 257, 401, 443, 467, 521, 571, 641, 653, 673, 797, 907, 911, 971, 983, 997, 1013, 1151, 1153, 1181, 1187, 1223, 1231, 1277, 1291, 1303, 1361, 1433, 1481, 1511, 1597, 1637, 1723, 1741, 1811, 1951, 2027, 2081, 2083, 2141, 2287, 2311

Offset: 1

Vincenzo Librandi, Jun 08 2014

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

Cf. A063908, A023204, A153507, A174363, A243595.

[p: p in PrimesUpTo(2500) | IsPrime(2*p^3 - 3)];

Select[Prime[Range[2500]], PrimeQ[2 #^3 - 3] &]

A252042 Primes p such that 2p^3 + 1 and 2p^3 + 3 are also primes.

Original entry on oeis.org

2, 29, 1709, 5849, 6857, 6959, 8999, 10139, 11909, 13127, 13877, 15077, 15749, 17657, 19457, 23357, 23399, 26729, 27407, 27479, 28349, 30047, 31907, 32957, 39569, 46559, 46589, 46817, 50417, 58757, 59219, 60737, 62207, 62687, 62819, 66947, 70589, 71237, 74699

Offset: 1

K. D. Bajpai, Dec 13 2014

nonn

			a(2) = 29 is prime: 2*29^3 + 1 = 48779 and 2*29^3 + 3 = 48781 are both primes.
a(3) = 1709 is prime: 2*1709^3 + 1 = 9982887659 and 2*1709^3 + 3 = 9982887661 are both primes.

K. D. Bajpai, Table of n, a(n) for n = 1..11485

Cf. A000040, A153507, A174363, A247101.

Select[Prime[Range[10000]], And[PrimeQ[2*#^3 + 1], PrimeQ[2*#^3 + 3]] &]
Select[Prime[Range[7500]],AllTrue[2#^3+{1,3},PrimeQ]&] (* Harvey P. Dale, Apr 03 2023 *)

s=[]; forprime(p=2, 10^5, if(isprime(2*p^3 + 1) && isprime(2*p^3 + 3), s=concat(s, p))); s

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A174363 Primes p such that 2*p^3 -+ 3 are also prime.

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A243595 Primes p such that 3 + 2*p^2 is also prime.

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A243630 Primes p such that 2*p^3 - 3 is also prime.

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A252042 Primes p such that 2*p^3 + 1 and 2*p^3 + 3 are also primes.

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A252042 Primes p such that 2p^3 + 1 and 2p^3 + 3 are also primes.