The Random Lines applet at: http://www.users.globalnet.co.uk/~perry/maths/othermaths.htm [Random Lines] has been updated to allow varying sizes of rectangles....
3700
Jon Perry
jonperryuk
Nov 1, 2001 11:52 am
The point is we have two words which mean exactly the same thing. I'm not going to force anyway to accept my usage, but I can't see any harm in the splitting...
3701
Juan Pedro Hecht
hecht@...
Nov 1, 2001 12:34 pm
Hello Paul, Thanks, you are right with the comment about the Boolean operator (E) 'belongs to', but it is not hard to obtain it from the primitive Boolean ...
3702
Phil Carmody
thefatphil
Nov 1, 2001 2:11 pm
(I don't have a cat) Most people wh've looked at deliberately finding pseudo-primes have done so to particular fixed small bases. i.e. Given base b, what...
3703
Jon Perry
jonperryuk
Nov 1, 2001 7:05 pm
If (p-1)!+1 is co-prime to p, then: [(p-1)!+1]^[p-1]=1modp So, j(p-1)!+1=kp+1 j(p-1)!=kp (p-1)!=xp which is a contradiction, therefore (p-1)!+1 always divides...
3704
Phil Carmody
thefatphil
Nov 1, 2001 7:23 pm
Just a quick question, what speed are people getting out of Jim's Gapper/CPAP combo? I remember seeing something like a search of 1100 billion being mentioned...
3705
Nuutti Kuosa
nkuosa
Nov 1, 2001 8:33 pm
It depends on number size. :-) number 2^116 + k, k from 1 to 4,000,000,000 sieving up to 752,500,739 took 15 min, using my P450 From sieving program : **...
3706
Nuutti Kuosa
nkuosa
Nov 1, 2001 8:41 pm
By the way. I have written small Excel macro that writes msdos bat files and those bat files keep my computers busy first running CPAPSieve.exe and then ...
3707
jfoug@...
jimfougeron
Nov 1, 2001 9:23 pm
... It also depends heavily on the memory in the PC. More memory, and CPAPSieve will process larger ranges, and you can possibly push the sieve a little...
3710
Shane
ttpi314159
Nov 1, 2001 10:00 pm
The folling is a conjecture, I've come up with. Prime Fibonacci and Lucas numbers, and their prime factors,2kp+/-1. When p= a small prime F(p) is prime, when...
3711
Nuutti Kuosa
nkuosa
Nov 1, 2001 10:29 pm
When selecting how high to sieve I have tried to balance these numbers (from my earlier posting) : ... I have calculated ratio 109872444 values left / 4598117...
3713
d.broadhurst@...
djbroadhurst
Nov 2, 2001 12:30 am
Shane Findley noted the following p for which ... The PrP F(104911) was discovered by Bouk de Water. See http:// ...
3714
d.broadhurst@...
djbroadhurst
Nov 2, 2001 1:43 am
A Konyagin-Pomerance proof of (1721^2161-1)/1720 6990 x32 01 Generalized repunit by Broadhurst, de Water and Leyland, is detailed in ...
3717
d.broadhurst@...
djbroadhurst
Nov 2, 2001 6:38 am
Phil is clearly deep into pseudoprimes. I have nothing of use to add. Marcel has already contributed more than I can say. Yet this thread has prompted a...
3718
David Cleaver
wraithx@...
Nov 2, 2001 7:07 am
Hello all, I don't know if this has been thought of before, or if its been investigated before (couldn't find any references on the net), but let me ask some...
3719
Phil Carmody
thefatphil
Nov 2, 2001 7:46 am
... There's a simple mapping from a posited C=A.B factorisation, where C is an odd composite such <A,B> -> <X,Y> where X^2-Y^2=C You then solve the problem in...
3720
Phil Carmody
thefatphil
Nov 2, 2001 8:04 am
... Note, however, that this linearity doesn't make the problem a simple one. One still has to brute-force through the set of primes. ... I thought about this...
3721
Satoshi TOMABECHI
tomabeti2000
Nov 2, 2001 8:32 am
David Cleaver wrote. ... It is possible to create the cubic sieve (CS). However it is probably slower than QS. (ax+b)^3-N is greater than (ax+b)^2-N. This fact...
3722
Phil Carmody
thefatphil
Nov 2, 2001 10:59 am
http://theregister.co.uk/content/55/22613.html 'DeCSS' DVD descrambler ruled legal. So the source-code illegal primes are no longer illegal. However, the...
3723
Nuutti Kuosa
nkuosa
Nov 2, 2001 4:27 pm
Here is the newest one : Found gap of 2028 at 2^116+5,766,300,710,013 to 2^116+5766300712041 digits : 35 and D = 25.22 I am going to check all k's in the range...
3724
Phil Carmody
thefatphil
Nov 2, 2001 4:35 pm
I'm sure many of us deal with large filter files and have to do tedious file operations on them to split or recombine files, or merge them, or filter them or...
3725
Phil Carmody
thefatphil
Nov 2, 2001 4:39 pm
... Something as simple as <<< ABC2 _your_initial_prime_here_ + $a a: from 0 to _your_gap_length_here_ ... should work. 'step 2' can be added to skip the...
3726
Nuutti Kuosa
nkuosa
Nov 2, 2001 4:52 pm
I tried this : ABC2 2^116+5766300710013+$a a: from 0 to 2028 and I got that : 2^116+5766300710013+0 is composite: (0.000000 seconds) and primeform.exe gave : ...
3727
Hadley, Thomas H (Tom...
kctom99
Nov 2, 2001 5:40 pm
... Interesting. I wanted to see which program was right so I used "factor.exe" (I forget where on the web this came from.) I found what appears to be a bug...
3728
jfoug@...
jimfougeron
Nov 2, 2001 6:02 pm
... used "factor.exe" ... to be a ... The factor.exe file certainly has bugs. it uses integer (or float) numbers when building expressions, instead of Miracl...
3729
Jon Perry
jonperryuk
Nov 2, 2001 6:16 pm
Fermat's Little Theorem, the well-known a^(p-1)=1modp, holds iff a and p are co-prime. So if a and p are not co-prime then the result is NOT 1modp, but xmodp, ...
3730
Jon Perry
jonperryuk
Nov 2, 2001 6:19 pm
If anyone is still interested, I added another applet to: http://www.users.globalnet.co.uk/~perry/maths/randomlines/randomlines.htm that displays random...
3731
jfoug@...
jimfougeron
Nov 2, 2001 6:33 pm
Short answer: This is a round off problem exhibited in release build 1.1 Long answer: In the 1.1 release of PFGW, when it builds the FFT's, it finds which FFT...
3734
Phil Carmody
thefatphil
Nov 3, 2001 1:15 am
... In the particular case I had in mind, GMP uses a random (odd?) number with the same number of bits as the number you're testing for its SPRP tests. i.e. a...
3735
Shane
ttpi314159
Nov 3, 2001 2:39 am
As a follow up, I noticed that potential factors of F(p)and L(p). Factors of F(p), must be 1,or 5 mod 8. Factors of L(p), must be 1,or 4 mod 5. Mersenne...
