Properties of Mersenne numbers

[science_man_88]

Originally Posted by CRGreathouse

What's the contradiction? 1 | 2, 2 | 2; 1 | 3, 1 | 3, 3 | 3; 1 | 5, 5 | 5.

0, 1, 1, 2, 3, 5,

Un can be prime only when n is prime.

3 primes in a row but not 3 prime indexes in a row so it doesn't fit

but this is a thread on mersenne I guess I have no point then.

[CRGreathouse]

Originally Posted by science_man_88

3 primes in a row but not 3 prime indexes in a row so it doesn't fit

but this is a thread on mersenne I guess I have no point then.

If you look at the actual divisibility property you'll see that it doesn't lead to a contradiction.

[science_man_88]

Originally Posted by CRGreathouse

If you look at the actual divisibility property you'll see that it doesn't lead to a contradiction.

but have 3 primes in row does! as it says Un can be prime only if n is prime basically which if you notice means for 3 primes to be in a row we would need 3 primes with difference 1 to exist can you name those three ?

[davar55]

Originally Posted by science_man_88

I wish finding primes in lucas sequences were easy lol, if so we could rely on the fact that mersenne numbers are U(3,2) if I remember correctly.

The connection between Fib, Lucas, and the primes was alluded to in
a thread in this forum (over two years old) in which a nice conjecture
was first presented by me. I'll look for it later if you can't find it and
are interested.

[science_man_88]

Originally Posted by davar55

The connection between Fib, Lucas, and the primes was alluded to in
a thread in this forum (over two years old) in which a nice conjecture
was first presented by me. I'll look for it later if you can't find it and
are interested.

Originally Posted by davar55

There's a thread (over two years old) in Math or Puzzles here in which I
presented a conjecture of mine relating Fib and Lucas sequences.

I'll look for it later if you can't find it.

It needed a big numeric test that no one pursued here.
You might be interested.

I'm told not to post double and someone else does ?

[davar55]

Originally Posted by ATH

Theorem checks out up to p=73, though thats not very far. Mersenne primes have 1 solution and composite numbers have 0 or 2:

p    (x,y) so 2p-1=4*x2+27*y2

5    1,1
7    4,1
11    no solution
13    23,15
17    181,1
19    149,127
23    no solution
29    no solution
31    23081,783
37    142357,45695 and 185341,1119
41:    no solution
43:    no solution
47:    no solution
53:    no solution
59:    no solution
61:    752652049,38443119
67:    4922679991,1369547633 and 5053371809,1297114833
71:    no solution
73:    no solution

The solution for 7 is (x,y) = (5,1) not (4,1).

[science_man_88]

Originally Posted by ATH

Theorem checks out up to p=73, though thats not very far. Mersenne primes have 1 solution and composite numbers have 0 or 2:

p	(x,y) so 2p-1=4*x2+27*y2

5	1,1
7	4,1
11	no solution
13	23,15
17	181,1
19	149,127
23	no solution
29	no solution
31	23081,783
37	142357,45695 and 185341,1119
41:	no solution
43:	no solution
47:	no solution
53:	no solution
59:	no solution
61:	752652049,38443119
67:	4922679991,1369547633 and 5053371809,1297114833
71:	no solution
73:	no solution

I see a link between the 2 that have 2 sets is this a bad thing ? look at sumdigits for the two sets of numbers highlighted

[CRGreathouse]

Looks like chance to me. Any reason to think otherwise?

[science_man_88]

Originally Posted by CRGreathouse

Looks like chance to me. Any reason to think otherwise?

not with the data provided.I've done a little more research into the numbers highlighted by calculator and I found that the multiplication of the digits of each one then taking sumdigits gives a multiple of 9 which as you know should come back to 9 if repeated.

[science_man_88]

(20:17)>for(y=1,9,forstep(x=y,1000,9,print1(multiplydigits(x)%9","));print())
1,0,0,7,3,6,7,6,3,7,0,0,0,8,5,0,2,2,0,5,8,0,0,0,5,6,3,5,3,6,5,0,0,0,0,0,3,0,0,3,0,0,0,3,0,0,2,5,0,5,2,0,0,8,8,0,0,2,3,3,2,0,0,6,2,6,0,0,0,6,0,0,0,6,0,0,6,0,0,5,5,0,0,8,2,0,2,8,0,0,8,0,0,3,8,6,6,8,3,0,0,0,0,0,0,0,0,0,0,0,0,0,
2,1,0,0,6,1,3,3,1,6,0,0,0,0,7,3,6,7,6,3,7,0,0,0,7,1,0,4,4,0,1,7,0,0,0,3,0,0,3,0,0,3,0,0,0,0,6,4,3,3,4,6,0,0,4,0,0,7,4,0,4,7,0,0,1,1,0,0,6,0,0,6,0,0,0,6,0,0,0,3,1,3,0,0,1,6,6,1,0,0,7,7,0,0,4,1,0,1,4,0,0,0,0,0,0,0,0,0,0,0,0,
3,2,2,0,0,5,8,0,8,5,0,0,1,0,0,6,1,3,3,1,6,0,0,0,0,5,6,3,5,3,6,5,0,0,0,6,6,0,6,6,0,6,6,0,0,0,1,3,6,1,6,3,1,0,0,0,0,3,5,6,6,5,3,0,0,5,0,0,3,3,0,3,3,0,0,3,3,0,0,1,6,6,1,0,0,3,1,3,0,0,6,5,6,0,0,5,3,3,5,0,0,0,0,0,0,0,0,0,0,0,0,
4,3,4,3,0,0,4,6,6,4,0,0,2,2,0,0,5,8,0,8,5,0,0,2,0,0,3,2,6,6,2,3,0,0,0,0,3,0,0,3,0,0,3,0,0,0,5,2,0,8,8,0,2,5,0,0,0,8,6,3,8,3,6,8,0,0,0,0,0,6,0,0,6,0,0,0,6,0,0,8,2,0,2,8,0,0,5,5,0,0,5,3,3,5,0,0,6,5,6,0,0,0,0,0,0,0,0,0,0,0,0,
5,4,6,6,4,0,0,3,4,3,0,0,3,4,3,0,0,4,6,6,4,0,0,4,4,0,0,1,7,0,7,1,0,0,3,0,0,0,3,0,0,3,0,0,0,0,0,1,3,6,1,6,3,1,0,0,0,4,7,0,1,1,0,7,4,0,0,0,6,0,0,6,0,0,6,0,0,0,0,6,7,3,3,7,6,0,0,7,0,0,4,1,0,1,4,0,0,7,7,0,0,0,0,0,0,0,0,0,0,0,0,
6,5,8,0,8,5,0,0,2,2,0,0,4,6,6,4,0,0,3,4,3,0,0,6,8,6,0,0,8,3,3,8,0,0,6,6,0,0,6,6,0,6,6,0,0,4,0,0,6,4,3,3,4,6,0,0,0,0,8,6,3,8,3,6,8,0,0,0,3,3,0,3,3,0,3,3,0,0,0,4,3,6,4,6,3,4,0,0,0,0,3,8,6,6,8,3,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,
7,6,1,3,3,1,6,0,0,1,0,0,5,8,0,8,5,0,0,2,2,0,0,8,3,3,8,0,0,6,8,6,0,0,0,3,0,0,0,3,0,0,3,0,0,8,8,0,0,2,5,0,5,2,0,0,5,0,0,3,5,6,6,5,3,0,0,0,0,6,0,0,6,0,0,6,0,0,0,2,8,0,5,5,0,8,2,0,0,0,2,6,3,2,3,6,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
8,7,3,6,7,6,3,7,0,0,0,0,6,1,3,3,1,6,0,0,1,0,0,1,7,0,7,1,0,0,4,4,0,0,3,0,0,3,0,0,0,3,0,0,0,3,7,3,0,0,7,6,6,7,0,0,1,1,0,0,7,4,0,4,7,0,0,6,0,0,0,6,0,0,6,0,0,0,0,0,4,3,6,4,6,3,4,0,0,0,1,4,0,7,7,0,4,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,8,5,0,2,2,0,5,8,0,0,0,7,3,6,7,6,3,7,0,0,0,0,3,2,6,6,2,3,0,0,2,0,0,6,6,0,6,6,0,0,6,6,0,0,7,6,6,7,0,0,3,7,3,0,0,6,2,6,0,0,2,3,3,2,0,0,3,3,0,0,3,3,0,3,3,0,0,7,0,0,6,7,3,3,7,6,0,0,0,0,2,6,3,2,3,6,2,0,0,0,0,0,0,0,0,0,0,0,0,0,

okay that doesn't narrow things down.