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
Keywords
Examples
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.
Links
- Harvey P. Dale and K. D. Bajpai, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)
Programs
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Magma
[p: p in PrimesUpTo(100000)|IsPrime(2*p^3-3) and IsPrime(2*p^3+3)]
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Maple
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
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Mathematica
Select[Prime[Range[5000]],And@@PrimeQ[2 #^3+{3,-3}]&] (* Harvey P. Dale, Jan 25 2013 *) -
PARI
forprime(p=1, 55000, if(ispseudoprime(2*p^3-3) && ispseudoprime(2*p^3+3), print1(p, ", "))) \\ Felix Fröhlich, Nov 27 2019
Comments