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Primes that generate 5 longer primes by prefacing their 5 successors in sequence.
1

%I #14 Jul 30 2013 05:47:58

%S 3687530993,4826397283,7724657491,9980308301,15974564917,28909417051,

%T 75268578271,80574464057,93244706063,99745568639,103152269047,

%U 142659491629,154807590677

%N Primes that generate 5 longer primes by prefacing their 5 successors in sequence.

%C This is similar to A219271, but the successor primes are here concatenated to the left rather than the right.

%e The primes following a(1)=3687530993 are 3687530999, 3687531007, 3687531011, 3687531019 and 3687531041, and each addition of these primes in sequence up through the final 60-digit 368753104136875310193687531011368753100736875309993687530993 yields a prime.

%o (PARI) [Output is a vector of 6 successive primes for each

%o element of the sequence, which is the smallest]

%o {

%o \\ This simple program checks modulo 3 first\\

%o p=[5,7,11,13,17,19];e=[10,10,100,100,100];

%o while(1,

%o if((p[1]+p[2])%3,f=1;for(i=2,5,

%o if((p[i]+p[i+1])%3,f=0;break()));

%o if(f,P=p[1]+p[2]*e[1];if(ispseudoprime(P),

%o E=e[1];for(i=2,5,E*=e[i];P+=E*p[i+1];

%o if(ispseudoprime(P)==0,f=0;break()));

%o if(f,print(p)))));

%o for(i=1,5,p[i]=p[i+1]);p[6]=nextprime(p[6]+1);

%o for(i=1,4,e[i]=e[i+1]);if(p[5]>e[5],e[5]*=10))

%o }

%Y Cf. A219271.

%K nonn,base

%O 1,1

%A _James G. Merickel_, Nov 25 2012

%E Terms missing in original added by _James G. Merickel_, Jul 25 2013