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A202136
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Prefixing digits to Mersenne primes to obtain larger primes.
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1
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13, 17, 131, 4127, 18191, 10131071, 1524287, 362147483647, 152305843009213693951, 58618970019642690137449562111, 57162259276829213363391578010288127, 55170141183460469231731687303715884105727
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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Mersenne prime + n*10^D with D = number of digits of the Mersenne prime.
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EXAMPLE
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For Mersenne4: -1 + 2^7 + 4*10^3 = 4127 which is prime.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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