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A202136
Prefixing digits to Mersenne primes to obtain larger primes.
1
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
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
Sequence in context: A356791 A289866 A210547 * A123909 A176555 A237423
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