- #1
ramsey2879
- 841
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ramsey2879 "Relate Mersenne Primes To Square Triangular Numbers" said:I managed to write a basic program using true/false arrays with binary like addition subtraction and multiplication that checked all Mersenne numbers, [tex]M_p = 2^{p} -1 \mid p = \mb{prime}[/tex] for primes from p = 3 up through p = 929 base upon the conjectured relation between Mersenne Primes and Square Triangular Numbers
I let my program run until it had checked the primeness of M(P) for first 160 odd primes (up through p = 929) and it correctly indicated whether M(p) is prime or not in this range for all odd primes.
My conjecture that if p is odd then M(p) is prime if and only if [tex]S_{2^{p-1}} == 1 \mod M(p) proved correct for each of these 160 odd primes. p = 2 is excluded from my conjecture since M(p) = 3 is a factor in my recursive formula for S_{2^{p-1}} where S_{n} squared is the nth square triangular number.
Is it correct to say that there is less than a (1/2)^(160) probability that my conjecture is false and that a counter example exists for an odd prime? Assuming that no one finds a counter example of course
2.
If this probability is expressed as a decimal number, how many zeros come between the first non zero digit and the decimal point?