A235167 Primes which are the sum of the first k consecutive composite numbers and such that the sums of the first k+1, k+2 and k+3 consecutive composites are also prime.
1041973527756883, 1367813419317223, 2061752246097991, 2952443719006597, 3103011021307399, 3372968619197677, 10155190978946137, 34071498970634821, 43003872349213873, 45743947962658333, 58096932030228859, 60092475306807649, 115486262684753671
Offset: 1
Keywords
Examples
a(1) = 1041973527756883 is the least prime, sum of the first consecutive 44208182 composites from 4 to 47042265, and such that the sum of the first 44208183, 44208184 and 44208185 composites are 1041973574799149, 1041973621841417, 1041973668883687, all prime.
Programs
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PARI
i=0; b=0; for( a=2, 2*10^8, if( !isprime(a) , i=i+1; b=b+a; if(( isprime(b) &a%2==1& isprime(b+a+1)) &isprime(a+2)& isprime(b+2*a+4)&isprime( a+4)&isprime(b+3*a+9), print1(b,", "))))
Extensions
a(8)-a(13) from Donovan Johnson, Jan 06 2014