# mersenne

1. ### Mersenne Primes

Mersenne Primes are prime numbers derived from the formulae (2**x)-1, but this only works when x is also a prime number. However, this is not always the case, for example, when x = 11 the resultant number (2,047) is not prime, because 2047 has prime factors of 23 and 89, which are multiples of...
2. ### 8th perfect number and 9th Mersenne prime

In the Wiki list of OEIS sequences, both the 8th perfect number and 9th Mersenne prime agree for their first 9 digits, but essentially not the rest. Is this anomaly mathematically explainable? Please see https://en.wikipedia.org/wiki/List_of_OEIS_sequences
3. ### Multiplicative Congruential Generator Code

Hey guys! I'm new here. I've a pressing homework due, someone help! I'm looking for a C/C++/Fortran code for a Multiplicative Congruential Generator for the Mersenne Prime m = 2^8 - 1 = 31. Any help is hugely appreciated! Can't promise to mention your credits on my homework assignment...
4. ### Multiplicative Congruential Generator Code

Hey guys! I'm new here. I've a pressing homework due, someone help! I'm looking for a C/C++/Fortran code for a Multiplicative Congruential Generator for the Mersenne Prime m = 2^8 - 1 = 31. Any help is hugely appreciated! Can't promise to mention your credits on my homework assignment...
5. ### Mersenne^Mersenne prime number test

a,b,n,(n-1),p out of N and n=2^p-1 := Mersenne Prime The prime a^p-b^p identity holds if p is prime a^p-b^p= (a-b)(a^(p-1)+a^(p-2)*b^1+a^(p-3)*b^2+a^(p-4)*b^3.....+a^1*b+b^(p-1)) 2^p-(2-1)^p ; p=7 = 2^3-1 is Mersenne prime for Mersenne p=7= 2^3-1 Proof: 2^7-1^7 =...
6. ### Mersenne Prime - Interesting Observation

I am not sure if this has been proven or is really true for all Mersenne Primes: - If (2 ^ k) - 1 is a Mersenne Prime then (2 ^ k) + 1 is not a prime, for k > 2.
7. ### Mersenne Primes and Goldbach Conjecture

Since we know that if ((2^a)-1) is prime, 'a' is also prime, couldn't we conjecture that ((2^a)-1)*((2^b)-1) = 2^c - 2^a - 2^b + 1 simplified to 2^a * 2^b = 2^c, where 'a' and 'b' are prime numbers, and 'c' is even. simplified to a + b = c If it is conjectured that there are an...
8. ### Mersenne Primes (easy)

Seeing the latest started me thinking. OEIS A113656 lists the digits of the Mersenne Prime exponents. Pretty simple question. If one does a running average of the digits of the Mersenne Prime exponents, what is the expected value? I have a few observations. Generally, the digits are "random"...
9. ### Mersenne numbers

I am trying to read the proof of a theorem by Rotkiewicz about pseudoprimes but I'm stuck. If p and q are prime, and M_p M_q \equiv 1 mod pq then M_p M_q \mid 2^{pq} -1\mid 2^{M_p M_q -1} -1 But why?
10. ### Every Mersenne number 2^p-1 is square free.

Every Mersenne number 2^p-1 is square free. Is every Mersenne number 2^p-1 square free? Yes, It is. Every Mersenne number 2^p-1 is square free. Proof: It is easy to show that the square of every odd number 2n+1 is: (2n+1)^2 = 4n^2+4n+1 = 4(n^2+n)+1, has 4k+1 shape. But every Mersenne...
11. ### Some Properties of Mersenne Number Factors ?

If M_p is Mersenne number of the form M_p=2^p-1 is it true that : a) (q=k\cdot 2^3+1 \wedge M_p\equiv 0 \pmod q)\Rightarrow (k\equiv 0 \pmod p \wedge \gcd(k-1,3)=1) b) (q=k\cdot 2^3-1 \wedge M_p\equiv 0 \pmod q)\Rightarrow (4k\equiv 1 \pmod p \wedge \gcd(k+1,3)=1)
12. ### Mersenne numbers

Hello. I've got three questions. 1.Can a Mersenne number be a multiple of another Mersenne number? Prove. (I mean is that possible that 2^a - 1 | 2^b - 1 where a, b are prime numbers) 2.Can a Mersenne number be equal to X^n ? (X and n are integer). Prove. (This Mersenne number is 2^d - 1 where d...
13. ### Mersenne number

I came across this question which I have failed to do.Prove that if n is a positive integer,n>1,then Mersenne number Mn cannot be the power of a positive integer.Assist me on this please.
14. ### Mersenne Prime Finder Program

Hey everyone, I randomly woke up this morning thinking about prime numbers... so I wrote a program in Java to find a user specified number of Mersenne Primes. Maybe that sounds dumb, because I know there are lots of people trying to find larger and larger primes... but I was curious to see what...
15. ### Mersenne and Fermat Numbers congruence

f(x)=Mod( \phi(x),\sigma_0(x))\: , \; x\in {N_{*}^{+}} Applying this function to Mersenne and Fermat numbers, I've seen that this congruences seems to fulfill: \phi(F_n) \equiv 0\; (mod \sigma_0(F_n))\\ \phi(F_n-2) \equiv 0\; (mod \sigma_0(F_n-2))\\ \phi(M_n) \equiv 0\; (mod \sigma_0(M_n))\\...
16. ### TWO new Mersenne primes found?

http://mersenne.org/ is currently reporting the discoveries of the 45th and 46th known presumptive Mersenne primes. This is an amazing streak!
17. ### New Mersenne numbers conjecture

Is anyone able to find the demonstration of the following Mersenne conjecture? for j=3, d=2*p*j+1=6*p+1 divide M(p)=2^p-1 if and only if d is prime and mod( d,8 )=7 and p prime and there exists integer n and i such that: d=4*n^2 + 3*(3+6*i)^2 This conjecture has been numericaly...
18. ### "recurrent" mersenne primes

Is there a prime p for which M(p) = 2^p-1 is prime, and also M(M(p)), and also M(M(M(p))), etc.? Imagine if there was such a prime for which M(p) was always prime... the days of GIMPS would be well over! Hehe.
19. ### are all mersenne primes also fibonacci?

and can it be proven?