A133560 Primes which have a partition as the sum of squares of seven consecutive primes.

1543, 3271, 4519, 7591, 9439, 11719, 23599, 39631, 45319, 51031, 56599, 90199, 151471, 173359, 210319, 222919, 235159, 261463, 313879, 367711, 402511, 459223, 478831, 499711, 610567, 634327, 732967, 760519, 819319, 883087, 939439, 968959

Offset: 1

Author

Artur Jasinski, Sep 16 2007

Keywords

• nonn

Comments

For sums of squares of two consecutive primes, only 2^2 + 3^2 = 13 is prime.

For sums of squares of three consecutive primes (see A133529), it seems that only 3^2 + 5^2 + 7^2 = 83 is prime.

Sums of squares of four (and all even numbers of) consecutive primes are even numbers except for 2^2 + 3^2 + 5^2 + 7^2 = 87 = 3*29, which is not prime.

For sums of squares of five of consecutive primes see A133559.

For every prime p > 3, p^2 mod 3 = 1, so the sum of the squares of any 3 such primes will be divisible by 3. - Jon E. Schoenfield, Sep 04 2023

Examples

			a(3)=4519 because 13^2 + 17^2 + 19^2 + 23^2 + 29^2 + 31^2 + 37^2 = 4519 is prime.
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A133529, A133538, A133559, A133561.

Programs

Maple

select(isprime,[seq(add(ithprime(n+k)^2,k=0..6),n=1..80)]); # Muniru A Asiru, Jul 19 2018

Mathematica

b = {}; a = 2; Do[k = Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a + Prime[n + 3]^a + Prime[n + 4]^a + Prime[n + 5]^a + Prime[n + 6]^a; If[PrimeQ[k], AppendTo[b, k]], {n, 1, 100}]; b
(* Second program: *)
Select[Map[Total, Partition[Prime@ Range@ 80, 7, 1]^2], PrimeQ] (* Michael De Vlieger, Jul 20 2018 *)