# [seqfan] A103807 and negative primes

Klaus Brockhaus klaus-brockhaus at t-online.de
Sun Mar 21 09:53:40 CET 2010

```Dear Zak and other SeqFans,

below you find an edited version (not yet submitted) of A103807. A103805
and A103806 should be edited similarly.

I  added both a PARI and a MAGMA program, because a comparison of PARI
and MAGMA might help to settle the quarrel about negative primes.

For PARI -23 is of type "t_INT", that is, an integer, or simply a
number. -23 is not a prime (integer), but the negative value of prime
(integer).
For MAGMA -23 is of type "RngIntElt", that is, an element of the ring of
integers. -23 is a prime element of the ring of integers.

Regards
Klaus

%I A103807
%S A103807
2,5,7,23,37,103,313,457,733,863,2053,2063,2917,4723,7187,7817,8017,
%T A103807
9007,9473,9973,10687,11527,11923,13477,13883,15787,26833,31477,34897,
%U A103807 36097,36353,36493,39937,44417,46447,47623,52103,53377,55813,60737
%N A103807 Primes p such that 2*p-27, 2*p+27, 2*p-33 and 2*p+33 are
primes or negative values of primes.
%C A103807 Intersection of A103805 and A103806.
%t A103807 Intersection[Select[Range[100000], PrimeQ[ #
]&&PrimeQ[2#+33]&&PrimeQ[2#-33]&&PrimeQ[
# ]&&PrimeQ[2#+27]&&PrimeQ[2#-27]&]]
%o A103807 (MAGMA) [ p: p in PrimesUpTo(61000) | IsPrime(2*p-27) and
IsPrime(2*p+27) and IsPrime(2*p-33) and IsPrime(2*p+33) ];
%o A103807 (PARI) {forprime(p=2, 61000,
if(isprime(abs(2*p-27))&&isprime(2*p+27)&&isprime(abs(2*p-33))&&isprime(2*p+33),
print1(p, ", ")))}
%Y A103807 Cf. A103805, A103806.
%K A103807 nonn
%O A103807 1,1
%A A103807 Zak Seidov (zakseidov(AT)yahoo.com), Feb 16 2005
%E A103807 Definition clarified, comment adjusted, MAGMA and PARI
program added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar
21 2010

```