86225219*5259738299*5949540043*12482997260297*(2^43112609-1) is the largest known completely factorized superpseudoprime, discovered by Edson Smith ...
20974
djbroadhurst
Oct 2, 2009 5:02 pm
A base-b superpseudoprime is a non-semiprime composite number all of whose composite divisors are base-b pseudoprimes. ...
20975
Di Maria Giovanni
calimero22
Oct 2, 2009 5:11 pm
Hi How can i perform this expression: (2^(2^61-1)-1) mod 223 with GMP library? What's the C function sequence? Thank you Giovanni...
20976
maximilian_hasler
maximilian_h...
Oct 2, 2009 5:27 pm
... in PARI, use Mod(2,223)^(2^61 % eulerphi(223) -1) - 1 %146 = Mod(14, 223) i.e. MM61 = 14 (mod 223) Since 223 is prime, the exponent can be reduced mod...
20977
djbroadhurst
Oct 2, 2009 6:14 pm
... According to Landon Curt Noll and Tony Forbes, MM61 is not divisible by any prime less than 43180130614086110782608760243 ...
20978
Norman Luhn
nluhn
Oct 2, 2009 6:51 pm
More also here: http://anthony.d.forbes.googlepages.com/mm61prog.htm Norman...
20979
mgrogue@...
mgrogue
Oct 2, 2009 7:46 pm
... Geoff Reynolds and I wrote a program that is faster than Tony's, but he has not responded to our inquiries to see if he is interested in our code. --Mark...
20980
Lowell Rice
lowellcrice
Oct 2, 2009 9:11 pm
I'm new to this whole concept of talking about only primes, but I randomly came up with a formula to help find just some random primes. It may seem...
20981
marku606
Oct 3, 2009 1:22 pm
... I would like to hear more after you investigate further. You may or may not be aware that every prime of the form 8n + 1 and 8n + 5 can be written as a sum...
20982
djbroadhurst
Oct 3, 2009 2:24 pm
... 45 = 3^2 + 6^2 is not a prime or a power of a prime David...
20983
Norman Luhn
nluhn
Oct 3, 2009 2:43 pm
I glad to inform you, that maybe the first gigantic certificate with PRIMO is available in 50 days :-). So the elapsed time will be about 115 days. happy...
20984
maximilian_hasler
maximilian_h...
Oct 3, 2009 3:09 pm
... nor is 10=1^2+3^2. See http://www.research.att.com/~njas/sequences/A025284 Numbers that are the sum of 2 nonzero squares in exactly 1 way. Maximilian...
20985
mikeoakes2
Oct 3, 2009 3:37 pm
... My certification (strictly single-processor, which I understand yours is not) is down to just over 19000 bits, and reducing at about 1500 per week. Given...
20986
Norman Luhn
nluhn
Oct 3, 2009 4:16 pm
Oh yes, Mike ! But Phase 2 will be done also. I have at the moment 26921/33549 bits left. Still enough to do ! Norman [Non-text portions of this message have...
20987
Norman Luhn
nluhn
Oct 3, 2009 4:24 pm
Oh yes, Mike ! But Phase 2 will be done also. I have at the moment 26921/33549 bits left. Still enough to do ! Norman...
20988
marku606
Oct 3, 2009 4:48 pm
... That's the problem with posting in haste, I forgot to mention a couple of things outright: 1) I was assuming Lowell's constraint that the two squares are...
20989
marku606
Oct 3, 2009 6:47 pm
... Just checked up to 300,000 for numbers of the form 8n+5: 6531 of such numbers are primes or prime powers, and they can all be written as the sum of two...
... 6531 of such numbers are primes or prime powers, and they can all be written as the sum of two relatively prime squares only once. It appears that numbers...
20992
Kermit Rose
kermit1941
Oct 4, 2009 1:27 am
Hello. Because of an alternative factoring algorithm I am working on, the following speculation occurred to me. I know that it is not wise to state a...
20993
marku606
Oct 4, 2009 1:44 am
... Yes, of course. :) Simplicity is one thing; understanding the simple can be downright elusive to the untrained. Thank you David for your explanation. By...
20994
Lio David
maths_forall
Oct 4, 2009 2:51 pm
Puzzle: find the next square number after 2^n- 1 solution : (3*2^k)^2 note : k = (n-3)/2 example : ...
20995
djbroadhurst
Oct 4, 2009 3:17 pm
... That's rather easy when n is a positive even integer. Perhaps you might exercise some discipline and make clear the precise type of number "n" to which...
20996
Di Maria Giovanni
calimero22
Oct 4, 2009 3:45 pm
Hi to All I'm Giovanni Di Maria Maksym Voznyy, me and other people are running the "Repunit Project", to find next Repunit Prime Number. The results are on: ...
20997
Kermit Rose
kermit1941
Oct 4, 2009 4:21 pm
1d. Re: Formula Posted by: "marku606"; mark.underwood@... marku606 Date: Sat Oct 3, 2009 9:48 am ((PDT)) ... An integer z is a sum of two squares in...
20998
djbroadhurst
Oct 4, 2009 4:26 pm
... I am interested in the difference between the "componenti" and the "appassionati" at http://www.gruppoeratostene.com/ To my ear, the "appassionati" sound...
20999
Kermit Rose
kermit1941
Oct 4, 2009 5:00 pm
1g. Re: Formula Posted by: "djbroadhurst" d.broadhurst@... djbroadhurst Date: Sat Oct 3, 2009 3:53 pm ((PDT)) All this is very simply explained by...
21000
djbroadhurst
Oct 4, 2009 5:01 pm
In primenumbers@yahoogroups.com, ... This is clearly false. Simply consider 20 = 2^2 + 4^2. David...
21001
djbroadhurst
Oct 4, 2009 5:13 pm
... and then "Kermit Rose" mistakenly claimed ... with the irrelevant observations ... Note that 10^2 and 5^2 are not coprime. David...
21002
Bernardo Boncompagni
redgolpe
Oct 4, 2009 5:40 pm
... I am a native Italian speaker, and in this context I would translate "componenti" as "members" and "appassionati" as "friends". In the "componenti" page...
