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A240971 Primes p such that (p^2 + p + 1)/3 is prime. 4
7, 13, 19, 31, 43, 73, 97, 103, 127, 157, 199, 223, 241, 271, 409, 421, 661, 673, 727, 859, 883, 937, 1021, 1039, 1051, 1063, 1093, 1447, 1483, 1609, 1657, 1669, 1723, 1753, 1861, 1879, 1993, 2029, 2203, 2437, 2539, 2677, 2719, 2803, 2833, 2953, 3079, 3121 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Under Schinzel's hypothesis, there are infinitely many primes of this form.

p must be of form 6k+1 to give an integer. A053182 lists when p^2 + p + 1 is prime. - Jens Kruse Andersen, Aug 06 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..4900

Eric Weisstein's World of Mathematics, Schinzel's Hypothesis.

MAPLE

select(n -> isprime(n) and isprime((n^2 + n + 1)/3), [seq(6*k+1, k=1..1000)]); # Robert Israel, Aug 05 2014

MATHEMATICA

Select[Prime[Range[500]], PrimeQ[(#^2 + # + 1)/3] &]

PROG

(MAGMA) [p: p in PrimesInInterval(3, 3500)| IsPrime((p^2+p+1) div 3)];

(PARI) forprime(p=1, 10^4, s=(p^2+p+1)/3; if(floor(s)==s, if(isprime(s), print1(p, ", ")))) \\ Derek Orr, Aug 05 2014

CROSSREFS

Cf. A053182.

Sequence in context: A173176 A216550 A267803 * A023255 A122482 A265629

Adjacent sequences:  A240968 A240969 A240970 * A240972 A240973 A240974

KEYWORD

nonn

AUTHOR

Vincenzo Librandi, Aug 05 2014

STATUS

approved

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Last modified May 26 13:59 EDT 2022. Contains 354092 sequences. (Running on oeis4.)