June 24, 1992

This mailing contains both Update 2.6 and Page 65.

Several "Wanted" numbers were factored on Page 65. Using the number
field sieve algorithm, Bob Silverman factored the "Most Wanted" number
2,467- c133 and the "More Wanted" number 3,269- c123. Arjen Lenstra
factored the "More Wanted" number 2,487+ c147 with the elliptic curve
method. Arjen Lenstra and Mark Manasse, with the help of dozens of
other people and computers, factored the "More Wanted" number
3,311- c114 by the quadratic sieve algorithm. Arjen Lenstra and Mark
Manasse factored the "More Wanted" number 7,167- c111 using the
elliptic curve method. New wanted lists appear in Update 2.6.  As you
read these lists, note that 6,179-, 6,187-, 7,169- and 7,173- are the
"last" holes in their tables in our first edition. Silverman is factoring
2,479- c127 from the "Most Wanted" list of Update 2.5. That is why that
number is absent from the "Most Wanted" list of Update 2.6. On the other
hand, Lenstra and Manasse factored 7,167- after Update 2.6 was printed.

Arjen Lenstra factored two of the "Smaller but Needed" numbers, 11,140+ c98
and 12,139+ c100. Yuji Kida factored 2,830M c100, another of these numbers.
A new list of "Smaller but Needed" is given on the "champions" page.

The only numbers from the original 1925 Cunningham-Woodall tables which
have not yet been completely factored are a few base 2 numbers with
exponent < 500. Two of these numbers, 2,467- c133 and 2,487+ c147, were
factored on Page 65. As mentioned above, Silverman is doing 2,479- c127.
Only four of these numbers are not yet started. All four appear on the
"Most Wanted" list of Update 2.6.

There were several new champions for factoring Cunningham numbers on
this page.  Recall that a champion is one of the best two records in
its category. Arjen Lenstra, Mark Manasse and the network factored
3,311- c114, which was a record (second largest) for the quadratic
sieve method. Dave Rusin discovered a 42-digit factor of 10,201- by the
elliptic curve method. Bob Silverman set a new record of 58 digits for
largest penultimate prime factor when he factored 2,467-. We
congratulate these record holders.

The first holes done on Page 65 are in # 3306, 3310, 3337, 3338 and
3353. The second holes done on Page 65 are in # 3351, 3352 and 3354.
The only third hole done on Page 65 is in # 3302. The fourth holes done
on Page 65 are in # 3314, 3317, 3320 and 3347.  The only fifth hole
done on Page 65 is in # 3345.

The last 6LM number in the second edition was done by Arjen Lenstra.
See # 3349.

The smallest new factor reported on Page 65 has 22 digits. See # 3334.
A 28-digit factor of this number was known previously.

In late February, 1992, Slowinski and Gage discovered a new Mersenne
prime. The exponent is 756,839. This one is the thirty-second Mersenne
prime to be discovered and is the new largest known prime.

I have corrected several of your addresses recently. If you move,
please tell me.

Keep the factors coming!


Sam Wagstaff