Problems & Puzzles:
G. L. Honaker, Jr., asks for
a Mersenne prime (greater than 31=2^5-1) such that its reversal
I made a fast search looking
for Mersenne numbers (primes or composites) M(e)=2^e-1 such that
M(e) reversed is prime (as a matter of fact only Strongpseudo
prime) for e< 4369 and found that M(e) reversed
is prime for e= 5, 53, 189, 293, 1107, 2181, 2695, & 2871.
Q2. Please report any other e
such that M(e) reversed is prime.
is the largest Mersenne prime reversal that has been
successfully tested for primality?
J. K. Andersen wrote (May 08):
Q1 and Q3.
For the 41 known Mersenne primes 2^e-1 with e > 5, the reversal has
been proven composite by a negative prp test or finding a factor.
The 7 largest have a small factor. 7 divides the largest with e =
32582657. The largest performed prp test was at 909526 digits for e
= 3021377 which gives no factor below 10^10. PRP tests were made by
The reversal of 2^e-1 is a multidigit proven prime for e = 5, 53,
189, 293, 1107, 2181, 2695, 2871, and 7667. Primality proofs were
made by Marcel Martin's Primo. It is a probable prime for e = 19999,
27471, 44537, 62323, 134367, 174295, and no others below 213000.