A202136 Prefixing digits to Mersenne primes to obtain larger primes.

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

Offset

1,1

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

Links

Table of n, a(n) for n=1..12.

Henri Lifchitz and Renaud Lifchitz, PRP Top Records

Formula

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

Example

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

Prog

(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<<prime(n)-1); if(ispseudoprime(p), print1(ppfx(p), ", "))) } \\ Andrew Howroyd, Nov 17 2018

Crossrefs

Cf. A000668, A209385.

Sequence in context: A356791 A289866 A210547 * A123909 A176555 A237423

Adjacent sequences: A202133 A202134 A202135 * A202137 A202138 A202139

Keyword

nonn,base

Author

Gilbert Mozzo, Dec 12 2011

Extensions

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

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

Status

approved