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Old 2011-01-08, 12:07   #23
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Quote:
Originally Posted by CRGreathouse View Post
What's the contradiction? 1 | 2, 2 | 2; 1 | 3, 1 | 3, 3 | 3; 1 | 5, 5 | 5.
Quote:
0, 1, 1, 2, 3, 5,
Quote:
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.

Last fiddled with by science_man_88 on 2011-01-08 at 12:08
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Old 2011-01-08, 21:46   #24
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Quote:
Originally Posted by science_man_88 View Post
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.
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Old 2011-01-08, 22:13   #25
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Quote:
Originally Posted by CRGreathouse View Post
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 ?

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Old 2011-01-09, 16:15   #26
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Quote:
Originally Posted by science_man_88 View Post
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.
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Old 2011-01-09, 19:18   #27
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Quote:
Originally Posted by davar55 View Post
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:
Originally Posted by davar55 View Post
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 ?
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Old 2011-01-09, 20:38   #28
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Quote:
Originally Posted by ATH View Post
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 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).
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Old 2011-01-09, 21:56   #29
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Quote:
Originally Posted by ATH View Post
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 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

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Old 2011-01-09, 22:36   #30
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Looks like chance to me. Any reason to think otherwise?
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Old 2011-01-09, 22:39   #31
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Quote:
Originally Posted by CRGreathouse View Post
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.

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Old 2011-01-10, 00:15   #32
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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,
okay that doesn't narrow things down.

Last fiddled with by science_man_88 on 2011-01-10 at 00:18
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