Unit 1 - Whole Numbers - Chapter 4
... number we are factoring is even, then we keep using 2 as one of the factors until it is no longer even. Then we can try 3, then 5, then 7, then 11, and so on for succeeding prime numbers. But it is not really necessary to start with 2. If we were doing the prime factorization of 88, we might start w ...
... number we are factoring is even, then we keep using 2 as one of the factors until it is no longer even. Then we can try 3, then 5, then 7, then 11, and so on for succeeding prime numbers. But it is not really necessary to start with 2. If we were doing the prime factorization of 88, we might start w ...
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 ...