A219677 Primes that generate 5 longer primes by prefacing their 5 successors in sequence.

3687530993, 4826397283, 7724657491, 9980308301, 15974564917, 28909417051, 75268578271, 80574464057, 93244706063, 99745568639, 103152269047, 142659491629, 154807590677

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..13.

Example

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.

Prog

(PARI) /* Output is a vector of 6 successive primes for each
element of the sequence, which is the smallest */
{
\\ This simple program checks modulo 3 first\\
p=[5, 7, 11, 13, 17, 19]; e=[10, 10, 100, 100, 100];
while(1, if((p[1]+p[2])%3, f=1; for(i=2, 5, if((p[i]+p[i+1])%3, f=0; break())); if(f, P=p[1]+p[2]*e[1]; if(ispseudoprime(P), E=e[1]; for(i=2, 5, E*=e[i]; P+=E*p[i+1]; if(ispseudoprime(P)==0, f=0; break())); if(f, print(p)))));
for(i=1, 5, p[i]=p[i+1]); p[6]=nextprime(p[6]+1);
for(i=1, 4, e[i]=e[i+1]); if(p[5]>e[5], e[5]*=10))
}

Crossrefs

Cf. A219271.

Sequence in context: A094722 A283458 A234433 * A061441 A135915 A104330

Adjacent sequences: A219674 A219675 A219676 * A219678 A219679 A219680

Keyword

nonn,base,more

Author

James G. Merickel, Nov 25 2012

Extensions

Terms missing in original added by James G. Merickel, Jul 25 2013

Status

approved