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A243734 Primes p for which p + 4, p^2 + 4 and p^3 + 4 are primes. 1
3, 7, 103, 277, 487, 967, 4783, 5503, 5923, 8233, 21013, 26317, 27943, 41593, 55213, 78307, 78853, 86197, 89653, 94723, 99013, 123727, 148153, 157177, 166627, 172867, 177883, 179107, 185893, 192883, 194713, 203767, 204517, 223633, 225217, 227593, 236893 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is a subset of the sequences:

A023200: Primes p such that p + 4 is also prime.

A243583: Primes p for which p + 4 and p^3 + 4 are primes.

p is either 2 mod 5 or 3 mod 5, hence p^4 + 4 is 0 mod 5.

LINKS

Abhiram R Devesh, Table of n, a(n) for n = 1..1000

EXAMPLE

p = 3 is in this sequence because p + 4 = 7, p^2 + 4 = 13 and p^3 + 4 = 31 are all primes.

p  : p+4,  p^2+4,     p^3+4

7  :  11,     53,       347

103: 107,  10613,   1092731

277: 281,  76733,  21253937

487: 491, 237173, 115501307

PROG

(Python)

import sympy.ntheory as snt

n=2

while n>1:

....n1=n+4

....n2=((n**2)+4)

....n3=((n**3)+4)

....##Check if n1, n2 and n3 are also primes.

....if snt.isprime(n1)== True and snt.isprime(n2)== True and snt.isprime(n2)== True:

........print(n, " , " , n1, " , ", n2, " , ", n3)

....n=snt.nextprime(n)

(PARI) s=[]; forprime(p=2, 200000, if(isprime(p+4) && isprime(p^2+4) && isprime(p^3+4), s=concat(s, p))); s \\ Colin Barker, Jun 11 2014

CROSSREFS

Cf. A023200, A243583.

Sequence in context: A159310 A299377 A129660 * A158467 A260824 A028414

Adjacent sequences:  A243731 A243732 A243733 * A243735 A243736 A243737

KEYWORD

nonn,easy

AUTHOR

Abhiram R Devesh, Jun 09 2014

STATUS

approved

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Last modified February 26 05:19 EST 2020. Contains 332276 sequences. (Running on oeis4.)