" tommy quaternion "

[tommy1729]

https://math.stackexchange.com/questions...ne-numbers

For the extended mersenne numbers that are so cruxial here, I am looking for special cases :

4 conditions for X :

**
X = an extended mersenne number

**
X = a product of two extended mersenne numbers A and B, where 

A is a product of 2 primes C,D where C and D are extended mersenne numbers

 and B is a prime.

Or equivalent X = BCD where B,C,D are primes and extended mersenne numbers.

**
X is squarefree.

**
(X + 1)/4 is a prime P and P is NOT an extended mersenne number.

OR simplified :

3 conditions for X :


X = BCD where B,C,D are primes and extended mersenne numbers.

**
X is squarefree.

**
(X + 1)/4 is a prime P and P is NOT an extended mersenne number.

( notice primes of the form 4n + 1 are not extended mersenne numbers )

 

 
regards

tommy1729

Example :

3*7*31 = 651
651+1=652
652/4=163 (prime)

SO dimension 652 is a serious candidate for the desired algebra.

Now working in dimension 652 by hand and/or pocket calculator seems alot of work.
The idea of computers occurs ...

7*19*31 = 4123
4123+1 = 4124
4124/4 = 1031 (prime)

1031 is another candidate.


At the moment I see no easy way to test these dimensions.
In particular without a computer.

Although I have some ideas with iterations.



regards

tommy1729