MODIFIED MERSENNE NUMBERS AND PRIMES Several thousand

... 4, and 6 while for others such as for N=3 and 5 produce composite numbers. The French cleric Marin Mersenne(1588-1648) observed from these results that22-1=3, 23-1=7, 25-1=31, and 27-1=127 That is , if one takes two to a prime power p and subtracts one from the result , one will generate a higher pr ...

... 4, and 6 while for others such as for N=3 and 5 produce composite numbers. The French cleric Marin Mersenne(1588-1648) observed from these results that22-1=3, 23-1=7, 25-1=31, and 27-1=127 That is , if one takes two to a prime power p and subtracts one from the result , one will generate a higher pr ...

Number Theory III: Mersenne and Fermat Type Numbers

... M2 = 22 − 1 = 3, M3 = 23 − 1 = 7, M5 = 25 − 1 = 31, M7 = 27 − 1 = 127. This might lead one to conjecture that all Mersenne numbers in which the index n is prime, are prime. However, M11 turns out to be composite, so this conjecture is not true. • Record Mersenne primes: Nearly all of the record prim ...

... M2 = 22 − 1 = 3, M3 = 23 − 1 = 7, M5 = 25 − 1 = 31, M7 = 27 − 1 = 127. This might lead one to conjecture that all Mersenne numbers in which the index n is prime, are prime. However, M11 turns out to be composite, so this conjecture is not true. • Record Mersenne primes: Nearly all of the record prim ...