New largest prime number found

[ewmayer]

Originally Posted by akruppa

Didn't find any others < 10^12.

Alex

Shall we say "sort of nearly prime", then? Or mayhap, "Aspiring to primality but not quite there yet?"

Suggest we unleash the mighty Raman on the complete-factorization effort of this one.

[henryzz]

has anyone tried any p-1 yet

[ATH]

Originally Posted by ewmayer

Shall we say "sort of nearly prime", then? Or mayhap, "Aspiring to primality but not quite there yet?"

Suggest we unleash the mighty Raman on the complete-factorization effort of this one.

With 3 as a factor I would say its as far from prime as an odd number can be?

[ewmayer]

Originally Posted by ATH

With 3 as a factor I would say its as far from prime as an odd number can be?

Depends on how ones defines "far from prime"ness - I could argue that if it has only a few small factors and one very large [say > 90% the size of the original number] prime cofactor, it's "nearly prime". Think of finding a chunk of gold-bearing rock with 90% gold content - it's "nearly pure gold".

Raman-the Spaman, how's that SNFS polynomial selection coming? Don't keep us on tenterhooks, man - no time to be wasted!

[Mini-Geek]

Originally Posted by ewmayer

[say > 90% the size of the original number]

If a factor was >90% the size of the original number, wouldn't the original number divided by the factor be between 1 and 2? Perhaps > 90% the size of the square root of the original number (i.e. almost as large as a factor can possibly be).

[petrw1]

And if there is only one VERY LARGE remaining prime factor then it will be the largest prime every found

[henryzz]

the remaining number could in theory be prime

[ewmayer]

Originally Posted by Mini-Geek

If a factor was >90% the size of the original number, wouldn't the original number divided by the factor be between 1 and 2? Perhaps > 90% the size of the square root of the original number (i.e. almost as large as a factor can possibly be).

Uh, I think you mean the square root is as large as the *smallest* prime factor can possibly be. I mean 90% in terms of logarithmic factor size [roughly = number of digits for large factors], e.g. consider the complete factorization of the 11th Fermat number:

F₁₁ = 319489 . 974849 . 167988556341760475137 . 3560841906445833920513 . P564

There, the 4 small factors sum to 55 digits (thus their product must have <= this many digits), so the large cofactor satisfies the "> 90%" criterion. Thus, I assert that according to this criterion, F₁₁ is "nearly prime".

[bsquared]

Originally Posted by henryzz

the remaining number could in theory be prime

Indeed. And all you have to do to claim the EFF prize is factor the number!

[ewmayer]

Originally Posted by bsquared

Indeed. And all you have to do to claim the EFF prize is factor the number!

Exactly - why do you think I'm so eager to see "our man in Calcutta", the mighty Raman, get started on the SNFS?