M31 216091

Why are those primes general Mersennes? What is your definition of it?

Official definition:

Let t(x) be the highest power of 2 which divides x+1.
Then a(1)=3; a(n) is the least prime p for which t(p) > t(a(n-1)).

An easier way to look at them is by listing Riesel primes (k<2^n), in order of their size(digits),
R=3 7 11 23 31 47 79 127 191 223 239 383 479 607 863 1087 1151 1279...
n=2 3 2 3 5 4 4 7 6 5 4 7 5 5 5 6 7 8 ...

As you can see, Mersenne primes by default, always have the largest exponent n, up that particular point. So what about the others?
The procedure for the algorithm is to, "reduce to lowest terms".
Since ie, 1*2^7-1 is also equal to, 2*2^6-1, 4*2^5-1,
8*2^4-1, 16*2^3-1, 32*2^2-1, 64*2^1-1, and 128*2^0-1. The lowest term, of the multiplier(k), reveals a prime exponent(n) with Mersenne primes.

61051 216113 is prime!

Update of the contiguous sequence:
1 216091-1
62431 216093-1
97065 216095-1
16371 216098-1
55847 216100-1
48609 216101-1
22311 216103-1
6213 216107-1
20265 216109-1
74697 216110-1
122649 216111-1
61051 216113-1

There seems to be a large gap between primes here.
I have passed k=500,000 with n=216113.
It should hit one soon, and keep the average at about one prime per week.

I just noticed the strangest thing, ... when I opened up this forum, It loaded as if it were back 2004. I saw old messages about networked LLR, and moderators needed.


Anyways, a new prime!
287453 216114

Update:
1 216091-1
62431 216093-1
97065 216095-1
16371 216098-1
55847 216100-1
48609 216101-1
22311 216103-1
6213 216107-1
20265 216109-1
74697 216110-1
122649 216111-1
61051 216113-1
287453 216114-1

Update:
1 216091-1
62431 216093-1
97065 216095-1
16371 216098-1
55847 216100-1 5/11/05
48609 216101-1
22311 216103-1
6213 216107-1
20265 216109-1
74697 216110-1
122649 216111-1
61051 216113-1
287453 216114-1
185551 216115-1 7/18/05 New!