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Forum: FermatSearch 2018-07-17, 22:31
Replies: 37
Views: 15,767
Posted By siegert81
Potential primality of F33, F34, and F35

F33, F34, and F35 are the smallest Fermat numbers (of unknown primality) that could be prime.

I'm assuming that various researchers have attempted to factor them and that their attempts have been...
Forum: Factoring 2018-04-16, 22:34
Replies: 1
Views: 2,449
Posted By siegert81
Independent GPU factoring

My wish is to independently test a series of Proth numbers with a particular k > 10,000 over millions of n values. I have a computer with an Nvidia 1080 Ti GPU to factor such a range, but I don't...
Forum: Factoring 2018-01-29, 10:41
Replies: 31
Views: 4,658
Posted By siegert81
Oh, I get it now. I had it in my head that M ≡...

Oh, I get it now. I had it in my head that M ≡ x·y (mod p1·p2)

Whoops!

M2 ≡ x2 ≡ a (mod p1) and M2 ≡ y2 ≡ a (mod p2)

Therefore, since both p1 & p2 evenly divide (M2 - a), their product must...
Forum: Factoring 2018-01-28, 02:59
Replies: 31
Views: 4,658
Posted By siegert81
Why is \(M^2-a\) divisible by \(p_1\)?

Why is \(M^2-a\) divisible by \(p_1\)?
Forum: Factoring 2018-01-24, 05:29
Replies: 31
Views: 4,658
Posted By siegert81
CRGreathouse, I don't believe that my number (N)...

CRGreathouse, I don't believe that my number (N) is a square to begin with. I'm trying to factor N, not x.
Forum: Factoring 2018-01-24, 05:24
Replies: 31
Views: 4,658
Posted By siegert81
Thank you for this information. I will have to...

Thank you for this information. I will have to crack open my old number theory book and read through the section on quadratic residues and quadratic reciprocity again. When I first attempted to...
Forum: FermatSearch 2018-01-24, 04:35
Replies: 2
Views: 4,674
Posted By siegert81
Ah. Well, that solves that mystery... ...

Ah.

Well, that solves that mystery...

Thanks!
Forum: FermatSearch 2018-01-23, 11:36
Replies: 2
Views: 4,674
Posted By siegert81
A new factor of F11?!

When using Leonid Durman's "Fermat.exe version 4.4, beta" software, I got the following result:



I used the input "n = 14 to 14" and "k = 9 to 100000000"

The first two factors are known, but...
Forum: FermatSearch 2018-01-23, 11:21
Replies: 16
F12
Views: 9,060
Posted By siegert81
The original information could be useful if...

The original information could be useful if Euler's factorization method was attempted.

If N = A^2 + B^2 = C^2 + D^2, then N can be factored.
Forum: Factoring 2018-01-23, 10:29
Replies: 31
Views: 4,658
Posted By siegert81
I'd like to better understand this method and the...

I'd like to better understand this method and the underlying mathematics. Instead of 672, how about starting with a quadratic residue of 7. If x^2 = 7 (mod N) (for some tested x), then I understand...
Forum: Factoring 2018-01-22, 23:17
Replies: 31
Views: 4,658
Posted By siegert81
1,990,292,873 = 44,449 x 44,777 My TI-86...

1,990,292,873 = 44,449 x 44,777

My TI-86 graphing calculator program factored this number using Fermat factorization almost immediately.

1,990,292,873 = 44,613^2 - 164^2 = (44,613 + 164) x...
Forum: Factoring 2018-01-22, 22:21
Replies: 31
Views: 4,658
Posted By siegert81
Assume N = p*q is a semiprime and that B and N...

Assume N = p*q is a semiprime and that B and N are relatively prime. Then B^(N+1) must be congruent to B^(p+q) (mod N).

So let's use N = 77 = 7*11 and B = 2.
Then 2^(77+1) = 2^(7+11) (mod 77)...
Forum: Factoring 2018-01-22, 02:37
Replies: 31
Views: 4,658
Posted By siegert81
Interesting. Let's assume that 672 is a quadratic...

Interesting. Let's assume that 672 is a quadratic residue (mod N). How would we then know which trial factors to skip over, or how would we rapidly eliminate these trial factors?



I've never...
Forum: Factoring 2018-01-21, 12:37
Replies: 31
Views: 4,658
Posted By siegert81
Maximum number of prime factors (3 questions)

Hello, an amateur mathematician here...

Let's say we are interested in investigating a "random" large odd number we know next to nothing about like 1,990,292,873.

We then begin applying trial...
Forum: GPU Computing 2017-04-20, 06:48
Replies: 3
Views: 1,477
Posted By siegert81
Stand alone GPU programs?

Are there any programs available for NVidia GPUs that either sieve ranges of numbers (such as Proth numbers) or perform primality tests on numbers?

I've been using NewPGen and LLR to independently...
Forum: Miscellaneous Math 2017-04-18, 07:30
Replies: 44
Views: 3,896
Posted By siegert81
Aside from this kind of auction, is there any way...

Aside from this kind of auction, is there any way for prime numbers or new discoveries to be of financial value?

I recall "Prime Coins" being similar to BitCoin for digital currency, but I haven't...
Forum: Miscellaneous Math 2017-04-18, 07:27
Replies: 44
Views: 3,896
Posted By siegert81
When creating the auction, I failed to include an...

When creating the auction, I failed to include an "international shipping" option as there is nothing physical to ship. I did not know that this would block non-US customers. I will have to contact...
Forum: Miscellaneous Math 2017-04-16, 02:48
Replies: 44
Views: 3,896
Posted By siegert81
Prime number for sale on eBay

I've discovered a new large prime number, but I haven't revealed what it is. Instead, I'm trying to sell it (the numerical information) on eBay. The winner of the auction can claim credit for the...
Forum: Factoring 2016-05-27, 18:25
Replies: 12
Views: 2,948
Posted By siegert81
Yes, that's what I concluded today after using...

Yes, that's what I concluded today after using other numbers as input.

It takes about 35 seconds to factor a P30 x P40.
It took over 4 minutes to factor a P40 x P40.

Still, I'm left wondering...
Forum: Factoring 2016-05-27, 07:32
Replies: 12
Views: 2,948
Posted By siegert81
When I used the siqs command, yafu found the...

When I used the siqs command, yafu found the factors in 1.2792 seconds.
Forum: Factoring 2016-05-27, 03:33
Replies: 12
Views: 2,948
Posted By siegert81
Simple factoring challenge + questions

Can anybody factor this number?

684546173393988695179580947496349194528189263072759549878869521320029

If so, what program(s)/method(s) did you use, and how fast were you able to factor it?
...
Forum: Factoring 2016-02-15, 06:34
Replies: 4
Views: 2,062
Posted By siegert81
I've been wondering the same...

I've been wondering the same...
Forum: Math 2014-11-23, 13:47
Replies: 2
Views: 1,394
Posted By siegert81
Curious about the Suyama test

I understand that the Suyama test is used on Fermat number co-factors to see if they're prime.
What exactly is the Suyama test? How does it work?

Is there an equivalent test for generalized...
Forum: Math 2014-11-19, 10:11
Replies: 2
Views: 1,237
Posted By siegert81
How can I prove this PRP prime?

According to PFGW, 1816 x (2^3217 - 1) + 1 is a PRP.

(FYI: 2^3217 - 1 is a Mersenne prime.)

I thought PFGW would use Pocklington's test as N-1 is easy to completely factor.

Am I missing...
Forum: Math 2014-03-09, 16:03
Replies: 23
Views: 2,744
Posted By siegert81
Actually, I *DO* get it, but I used the letter p...

Actually, I *DO* get it, but I used the letter p instead of q, on accident.

If p is a prime factor of Mq, then 2^q is congruent to 1 (mod p). Any power of 2 that is congruent to 1 (mod p) must be...
Showing results 1 to 25 of 74

 
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