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A133560
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Primes which have a partition as the sum of squares of seven consecutive primes.
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3
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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a(3)=4519 because 13^2 + 17^2 + 19^2 + 23^2 + 29^2 + 31^2 + 37^2 = 4519 is prime.
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MAPLE
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select(isprime, [seq(add(ithprime(n+k)^2, k=0..6), n=1..80)]); # Muniru A Asiru, Jul 19 2018
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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