For the amusement of the record prime hunters

[a1call]

If a Mersenne number is not divisible by any Mersenne primes less than itself (as few as they are), then its exponent is a prime number.

[science_man_88]

Originally Posted by a1call

If a Mersenne number is not divisible by any Mersenne primes less than itself (as few as they are), then its exponent is a prime number.

if you count 2^1-1=1 they all work technically.

[CRGreathouse]

Originally Posted by a1call

If a Mersenne number is not divisible by any Mersenne primes less than itself (as few as they are), then its exponent is a prime number.

2^121 - 1 is not divisible by 2^2 - 1, 2^3 - 1, 2^5 - 1, 2^7 - 1, 2^13 - 1, 2^17 - 1, 2^19 - 1, 2^31 - 1, 2^61 - 1, 2^89 - 1 or 2^107 - 1.

[science_man_88]

Originally Posted by CRGreathouse

2^121 - 1 is not divisible by 2^2 - 1, 2^3 - 1, 2^5 - 1, 2^7 - 1, 2^13 - 1, 2^17 - 1, 2^19 - 1, 2^31 - 1, 2^61 - 1, 2^89 - 1 or 2^107 - 1.

doh my reading skills need work I thought that they said mersenne number for some reason doh.

[a1call]

Originally Posted by CRGreathouse

2^121 - 1 is not divisible by 2^2 - 1, 2^3 - 1, 2^5 - 1, 2^7 - 1, 2^13 - 1, 2^17 - 1, 2^19 - 1, 2^31 - 1, 2^61 - 1, 2^89 - 1 or 2^107 - 1.

Thank you for the counter example. SM is slipping.

[a1call]

Originally Posted by a1call

If a Mersenne number is not divisible by any Mersenne primes less than itself (as few as they are), then its exponent is a prime number.

If a Mersenne number is not divisible by any Mersenne numbers with a prime exponent less than itself (as many as they are), then its exponent is a prime number.

[science_man_88]

Originally Posted by a1call

SM is slipping.

not really you just don't think of 1 as a mersenne number but it is( dependent on which definition you use).

[a1call]

Originally Posted by science_man_88

not really you just don't think of 1 as a mersenne number but it is( dependent on which definition you use).

But it is not a prime number, nor it has a prime exponent. You are still assuming that I have written "mersenne numbers", where I had written "mersenne primes" or have written "mersenne numbers with prime exponents".
1 does not satisfy neither (or is it either? ) condition.

[science_man_88]

Originally Posted by a1call

But it is not a prime number, nor it has a prime exponent. You are still assuming that I have written "mersenne numbers", where I had written "mersenne primes" or have written "mersenne numbers with prime exponents".
1 does not satisfy neither condition.

okay I'll give you that though there was a time when 1 was considered prime. also your statement about the exponent is an equivalent to division on the natural numbers as if the exponents divide so will the mersenne numbers.

[a1call]

Originally Posted by science_man_88

okay I'll give you that though there was a time when 1 was considered prime. also your statement about the exponent is an equivalent to division on the natural numbers as if the exponents divide so will the mersenne numbers.

Yes-but and No, respectively. Yes-but we happen to be living in 21st century and No, that does not state that any Mersenne number exponents are primes( although it does entail that).

[Batalov]

Originally Posted by a1call

If a Mersenne number is not divisible by any Mersenne numbers with a prime exponent less than itself (as many as they are), then its exponent is a prime number.

That's a tautology.

What you just wrote is equivalent to: "If a number is not divisible by any prime less than itself, then it is a prime number". Where the first clause is equivalent to the definition of a prime number.

So what you wrote is: "If a number is prime, then it is a prime number". That's profound!