A202136 Prefixing digits to Mersenne primes to obtain larger primes.

13, 17, 131, 4127, 18191, 10131071, 1524287, 362147483647, 152305843009213693951, 58618970019642690137449562111, 57162259276829213363391578010288127, 55170141183460469231731687303715884105727

Offset: 1

Author

Gilbert Mozzo, Dec 12 2011

Keywords

• nonn
• base

Comments

The smallest prefixing digits for the Mersenne primes are given in A209385. - Gilbert Mozzo, Mar 07 2012

The next term a(13) has 160 decimal digits. - Andrew Howroyd, Nov 17 2018

Examples

			For Mersenne4: -1 + 2^7 + 4*10^3 = 4127 which is prime.
		

Links

• Henri Lifchitz and Renaud Lifchitz, PRP Top Records

Crossrefs

Cf. A000668, A209385.

Programs

PARI

ppfx(n)={my(w=10^(1+logint(n,10)), k=n+w); while(!ispseudoprime(k), k+=w); k}
{ for(n=1, 100, my(p=1<Andrew Howroyd, Nov 17 2018

Formula

Mersenne prime + n*10^D with D = number of digits of the Mersenne prime.

Extensions

a(7)-a(9) added by Gilbert Mozzo, Mar 07 2012

a(10)-a(12) from Andrew Howroyd, Nov 17 2018