A357909 Primes p such that p+6, p+12, p+18, 4*p+37, 4*p+43, 4*p+49 and 4*p+55 are also all primes.

408211, 6375751, 6433741, 6718471, 19134931, 25280791, 63908851, 67078801, 152418151, 159268561, 217697911, 236220991, 237943591, 334030981, 363246211, 392644921, 406249171, 410652031, 428032441, 476660281, 478441291, 502777111, 552727711, 552855001, 554201731, 693654721, 816050071, 877207141

Offset: 1

Author

J. M. Bergot and Robert Israel, Nov 09 2022

Keywords

• nonn

Comments

Start of a "sexy" prime quadruple (in the sense of A023271) such that 1 + the sum of the quadruple is the start of another "sexy" prime quadruple.

All terms == 1 (mod 30).

Examples

			a(1) = 408211 is a term because 408211, 408211+6 = 408217, 408211+12 = 408223, 408211+18 = 408229 are primes (a "sexy" prime quadruple), the sum of this quadruple is 4*408211+36 = 1632880, and 1632880+1 = 1632881, 1632880+7 = 1632887, 1632880+13 = 1632893, 1632880+19 = 1632899 is another "sexy" prime quadruple.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..115

Crossrefs

Cf. A023271.

Programs

Maple

Res:= NULL: count:= 0:
for p from 1 by 30 while count < 40 do
  if isprime(p) and isprime(p+6) and isprime(p+12) and isprime(p+18)
  and isprime(4*p+37) and isprime(4*p+43) and isprime(4*p+49) and isprime(4*p+55)
then Res:= Res, p; count:= count+1
fi
od:
Res;