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2011-01-08, 12:07   #23
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by CRGreathouse 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

2011-01-08, 21:46   #24
CRGreathouse

Aug 2006

3·1,993 Posts

Quote:
 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.

2011-01-08, 22:13   #25
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 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 ?

Last fiddled with by science_man_88 on 2011-01-08 at 23:12

2011-01-09, 16:15   #26
davar55

May 2004
New York City

5×7×112 Posts

Quote:
 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.

2011-01-09, 19:18   #27
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

203008 Posts

Quote:
 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.
Quote:
 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 ?

2011-01-09, 20:38   #28
davar55

May 2004
New York City

5·7·112 Posts

Quote:
 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: 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).

2011-01-09, 21:56   #29
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 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: 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

Last fiddled with by science_man_88 on 2011-01-09 at 22:00

 2011-01-09, 22:36 #30 CRGreathouse     Aug 2006 175B16 Posts Looks like chance to me. Any reason to think otherwise?
2011-01-09, 22:39   #31
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 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.

Last fiddled with by science_man_88 on 2011-01-09 at 23:03

 2011-01-10, 00:15 #32 science_man_88     "Forget I exist" Jul 2009 Dumbassville 26×131 Posts 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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