Hot tuna! -- a p75 and a p79 by Sam Wagstaff!

[Batalov]

A new ECM record by Sam Wagstaff!

970 p75 336842026814486816413712532665671525518487238461533945786937785048474675329 11^304+1 1G 3885593015 2012-08-02 Sam Wagstaff

The group order:
[ <2, 2>, <3, 1>, <5, 2>, <13, 1>, <41, 1>, <11971, 1>, <14923, 1>, <15887, 1>,
<16333, 1>, <119129, 1>, <970961, 1>, <3408437, 1>, <10882111, 1>, <38612713,
1>, <173109949, 1>, <1584686398147, 1> ]

Interestingly, the default B2 value for B1=173109999 is 1589274236566, which is just enough. (a minimalistic test in progress:
ecm -sigma 3885593015 173109999 < c227 > ECp75.txt
... and surely ...

GMP-ECM 6.4.2 [configured with GMP 5.0.2, --enable-asm-redc] [ECM]
Input number is 6604857068189252819730948667846433708170919682317463967174714319350148535968504700215131814737582542911409411528095995619903696877100287394595437895996885419119698970679814635893121 (181 digits)
Using B1=173109999, B2=1589274236566, polynomial Dickson(30), sigma=3885593015
Step 1 took 1208795ms
Step 2 took 278537ms
********** Factor found in step 2: 336842026814486816413712532665671525518487238461533945786937785048474675329
Found probable prime factor of 75 digits: 336842026814486816413712532665671525518487238461533945786937785048474675329
Probable prime cofactor has 107 digits

[Uncwilly]

I thought that you brought a P75 on-line in the hunt for primes.

[WraithX]

Originally Posted by Batalov

A new ECM record by Sam Wagstaff!

970 p75 336842026814486816413712532665671525518487238461533945786937785048474675329 11^304+1 1G 3885593015 2012-08-02 Sam Wagstaff

Wow!!! This is an amazing find! Congratulations Sam!

Now all we need is a p71 and a p74 ecm find to have all digit levels up to p75 represented.

[bdodson]

Originally Posted by WraithX

Wow!!! This is an amazing find! Congratulations Sam!

Now all we need is a p71 and a p74 ecm find to have all digit levels up to p75 represented.

Amazing. Not a Cunningham Champion, since it's from the 11-extension;
not the main tables? Meets the Brent condition of 2.2*factor < C181.

Still short of 256-bits? Guess now we can keep records for the
PS3 assisted ECM. Hot Tuna for sure. -Bruce

[Raman]

A p75 ecm factor from a 181 digit number? In my own opinion, it could have been done by using GNFS itself, rather than the effort needed, required to find away a 75 digit factor, away by using ecm.

As such, such a huge factor would have been productive enough to be able to have been rather-worthwhile although if in case that it had been emerged away, popped from a larger enough, harder-to-NFS number, finding away candidate like, such as the p70 digit factor from the 3,607+

[ixfd64]

In other news, M1061 was factored today, setting a new SNFS record. If two new records in one day isn't awesome, then I don't know what is.

[bdodson]

Originally Posted by Raman

A p75 ecm factor from a 181 digit number? In my own opinion, it could have been done by using GNFS itself, rather than the effort needed, required to find away a 75 digit factor, away by using ecm.
...

Judging by the factors remaining on the other recent extensions, we can
reasonably estimate that Sam would have spent no more than the effort
to find a p60; and certainly less than needed for 181-digit gnfs. Finding
ecm factors like this p75 (and my p70) is due to a large number of curves,
spread over a lot of input numbers; not by a disproportionate effort on
a single number. It is quite possible that no more than a t55 effort was
spent on this specific number before the p75 showed up (just lots-and-lots
of t55 efforts ...). -bdodson

[bdodson]

Originally Posted by bdodson

Amazing. Not a Cunningham Champion, since it's from the 11-extension; not the main tables? ...

Still short of 256-bits? ... -Bruce

Maple reports log[2] = 247.57, so this is a 248-bit prime? That's
2^247 < p75 < 2^248. Guess that means Arjen's 1024-bit RSA
key as a product of four 256-bit primes is still secure. -bd

In other late breaking news, Sam's agreed to have the
base-11 and base-5 main table extensions effective August 1.
We may now welcome the newest Cunningham Champion!

[Batalov]

And another one, this time a p79!

Still short of 256-bits? ... -Bruce

Not anymore! This is 260 bits, right here.

p:=2302872188505279576573535015926441913945044975483579529517513795897664211127797;
time GroupOrder(p, 3648110021);
 
[ <2, 2>, <3, 3>, <5, 1>, <17, 1>, <29, 1>, <31, 1>, <127, 1>, <197, 1>, <673, 1>,
<3947, 1>, <18481, 1>, <938939, 1>, <19305469, 1>, <26324929, 1>, <46026329, 1>,
<97707917, 1>, <138483313, 1>, <764489238641, 1> ]

[Andi47]

Originally Posted by Batalov

And another one, this time a p79!

Congratulations to Sam Wagstaff!!!