[QUOTE=CRGreathouse;245063]What's the contradiction? 1 | 2, 2 | 2; 1 | 3, 1 | 3, 3 | 3; 1 | 5, 5 | 5.[/QUOTE]

[QUOTE]0, 1, 1, 2, 3, 5,[/QUOTE]

[QUOTE]Un can be prime only when n is prime.[/QUOTE]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.

[QUOTE=science_man_88;245116]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.[/QUOTE]

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

[QUOTE=CRGreathouse;245179]If you look at the actual divisibility property you'll see that it doesn't lead to a contradiction.[/QUOTE]

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 ?

[QUOTE=science_man_88;244815]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.[/QUOTE]

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.

[QUOTE=davar55;245292]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.[/QUOTE]

[QUOTE=davar55;245288]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.[/QUOTE]

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

[QUOTE=ATH;244741]Theorem checks out up to p=73, though thats not very far. Mersenne primes have 1 solution and composite numbers have 0 or 2:


[CODE]p (x,y) so 2[sup]p[/sup]-1=4*x[sup]2[/sup]+27*y[sup]2[/sup]

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
[/CODE][/QUOTE]

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

[QUOTE=ATH;244741]Theorem checks out up to p=73, though thats not very far. Mersenne primes have 1 solution and composite numbers have 0 or 2:


[CODE]p (x,y) so 2[sup]p[/sup]-1=4*x[sup]2[/sup]+27*y[sup]2[/sup]

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,[COLOR="Red"]45695[/COLOR] and 185341,[COLOR="Red"]1119[/COLOR]
41: no solution
43: no solution
47: no solution
53: no solution
59: no solution
61: 752652049,38443119
67: 4922679991,[COLOR="red"]1369547633[/COLOR] and 5053371809,[COLOR="red"]1297114833[/COLOR]
71: no solution
73: no solution
[/CODE][/QUOTE]

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

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

[QUOTE=CRGreathouse;245362]Looks like chance to me. Any reason to think otherwise?[/QUOTE]

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.

[CODE](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,[/CODE]

okay that doesn't narrow things down.