Double Mersenne Primes
A double Mersenne number that is prime is called a double Mersenne prime. Since a Mersenne number Mp can be prime only if p is prime, (see Mersenne prime for a proof), a double Mersenne number can be prime only if Mp is itself a Mersenne prime. The first values of p for which Mp is prime are p = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127. Of these, is known to be prime for p = 2, 3, 5, 7; for p = 13, 17, 19, and 31, explicit factors have been found showing that the corresponding double Mersenne numbers are not prime. Thus, the smallest candidate for the next double Mersenne prime is, or 22305843009213693951 − 1. Being approximately 1.695×10694127911065419641, this number is far too large for any currently known primality test. It has no prime factor below 4×1033. There are probably no other double Mersenne primes than the four known.
Read more about this topic: Double Mersenne Number
Famous quotes containing the word double:
“Society’s double behavioral standard for women and for men is, in fact, a more effective deterrent than economic discrimination because it is more insidious, less tangible. Economic disadvantages involve ascertainable amounts, but the very nature of societal value judgments makes them harder to define, their effects harder to relate.”
—Anne Tucker (b. 1945)