April 17, 1998, Nancy (France)

	Hello everybody,

this is the 3rd ecmnet newsletter, which appears each month. Previous
newsletters are available on the ecmnet home page [1]. We welcome new
participants: Alex Stuebinger, who ported GMP to the transputer,
Warut Roonguthai, and Nik Lygeros.

New factors found since last month include:

4106103682516222963030438446469563721 divides 731^60+1 Aiichi Yamasaki
142123048270447797297041447256894663487 divides p(14387) Paul Z.
2143603951224073791827147 divides 33^137+1 Samuli Larvala
33433415486316101708618060161 divides 45^140+1 Samuli Larvala
771765128032466758284258631297 divides RSm(50) Ralf Stephan
789705772829428743253863253835849 divides 17^124+1 Samuli Larvala
332817722770314187794325446534549089 divides 2^613-1 Paul Z.
1572295532075714459521547797 divides W(849) Paul Leyland
19082282834381130613 divides W(891) Paul Leyland
9144205714687032445758003941 divides F(1351) Ralf Stephan
6399032721246153065183 divides RSm(61) Ralf Stephan
10829601768590858922799569083910271 divides 6^345+1 Alex Stuebinger
591082109095345424416413908752729 divides 10^381-1 Torbjorn Granlund
118420287267066844820208926433723871 divides 2^661-1 Conrad Curry
1786946360382838276990549597027 divides 10^351-1 Torbjorn Granlund
4832227158939716614468345433242909 divides 10^286+1 Torbjorn Granlund
76232914055207003005318654163381 divides 10^326+1 Torbjorn Granlund
733682355979450871730022615216673064893 divides 2^1154+1 Paul Z.
2379400136516862886998624270185035447811 divides W1(229) Aiichi Yamasaki

There was one new champion (factor of 40 digits or more) found by GMP-ECM,
namely the factor of 40 digits of W1(229), the numerator of 1+1/2+...+1/229,
found by Aiichi Yamasaki during the Easter week-end. During this week-end,
Peter Montgomery was also lucky with his ecmfft program, as he found three
new champions:

prp41 36345637656251647357558267023272022549061 divides 19^129 - 1
prp40 7754171527028991249837121031071014622681 divides 68^108 + 1
prp41 13162699482819899846764424209701265149361 divides 44^120 + 1

In the Cunningham tables, ECMNET factored one "more wanted" number (2^1154+1)
and one fourth hole (2^613-1).

New top-100 page. As suggested by Torbjorn Granlund, the ecmnet page now
contains a link to a new "top-100" page, which contains the 100 largest
factors found by GMP-ECM. It has only 70 entries or so currently, and the
smallest one is a p19. Please submit new factors to this top-100 page !

Mersenne numbers. Two new numbers were factored: M613 and M661 (see above),
respectively 2nd and 8th smallest unfactored Mersenne numbers, from Will
Edgington table. Peter Montgomery noticed that the p36 factor of M613 
could have been found by the P-1 method, and suggests that the smallest
Mersenne numbers were not enough tested with the P-1 method. Conrad Curry
is currently testing (by ECM) the numbers in the M600-M700 range.

Repunits. Torbjorn Granlund found several new factors of 10^n+1 and 10^n-1,
in particular a p31 of 10^351-1, a p34 of 10^286+1 and a p32 of 10^326+1.

Fibonacci numbers. Ralf Stephan factored F(1351) (see above). It remains now
61 composites in the 1350-1500 range.

New numbers to factor. The ecmnet page now includes Crandall numbers, which
are of the form 2^((q-1)/2)+1 or 2^((q-1)/2)-1 (the one divisible by 3).
The factorizations for q=5807, 10501, 10691, 11279, 12391, 14479, 42737, 
83339, and 95369 are most wanted (contact Richard Crandall for more details).
I've added also some links to tables of Wolstenholme and cyclotomic numbers.

Smarandache and reverse Smarandache numbers. Ralf Stephan wrote a very nice 
paper about those strange numbers, which he tried to factor up to index 80.
Look at the Smarandache entry on the ecmnet page for a pointer to his paper.

New ecmgo program. Ralf Stephan wrote a program named ECMGO which automatically
computes the group order of a successfull curve, directly from the GMP-ECM log.
Check out on the bottom of the ecmnet page.

Warut Roonguthai improved the ecmloop.bat batch file for Windows/MSDOS
so that it stops as soon as a factor is found, like the Unix version.
Also, Conrad Curry improved the MSDOS binary of 14% for numbers of about
900 digits, and of 55% for numbers of 200 digits.

David Campeau and Jean-Charles Meyrignac have included GMP-ECM into a
Windows program named Factor98, which already included a P-1 factorizer.
As video games programmers, they are used to program in assembler.

[1] The ecmnet home page: http://www.loria.fr/~zimmerma/records/ecmnet.html