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A235165
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Primes which are sum of the first k consecutive composite numbers and such that the sum of the first consecutive k+1 composites and the sum of the first k+2 consecutive composites are also prime.
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2
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997, 3889, 320375057, 423704707, 3431156159, 11650632419, 15909713927, 16906981181, 18170097067, 19703643541, 25534764667, 65405464363, 89483860811, 96873744973, 157599307213, 161983109531, 250812627893, 255555662521, 304165468751, 506667567067, 563313151277, 641930941499, 719915546257, 755132545199, 988899991367, 1002877111091, 1013997492671
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(1) = 997 is prime and sum of the first 35 composites from 4 to 51.
And 997 + 52 = 1049 is prime and 1049 + 54 = 1103 is prime. But 1103 + 55 is even and thus not prime.
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MATHEMATICA
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Select[Partition[Accumulate[Select[Range[20*10^6], CompositeQ]], 3, 1], AllTrue[ #, PrimeQ]&][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 30 2017 *)
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PROG
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(PARI) i=0; b=0; for( a=2, 2*10^6, if( !isprime(a) , i=i+1; b=b+a; if(( isprime(b) & isprime(b+a+1) &isprime(a+2)& isprime(b+2*a+4))||(isprime(b)&isprime(a+1)&isprime(b+a+2)&isprime(a+3)&isprime(b+2*a+6)), print1(b, ", "))))
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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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