🚀 go-pugleaf

Arjen Lenstra and I are pleased to announce the record non-networked
factorization of a difficult number (no prime factors under 40 digits).
The number is (2^488 + 1)/257. Its prime factors are p_49 and p_97,
where
  
  p_49 = 1035817877926014488587133818491976759389034764353

and

  p_97 = 3002073757428777382273857922385512797763792723266417656025\
	 021527116989779952950182556537541850817.

We carried out the bulk of the computation in under ten days on a MasPar
SIMD computer with 16384 processors at Bellcore. We also used under a
day of CPU time on a DEC workstation. The entire factorization took
approximately a month and a half real time.

This should be compared with the overall record factorization of a
difficult number, namely 2^512 + 1, which took four months real time on
approximately 700 workstations around the world, together with a
65536-processor Connection Machine in one stage.

This computation can be seen as a substantial step towards a practical
implementation of the general number field sieve (GNFS): it depended on
character columns and a square root inside the algebraic number field
rather than explicit generators of the unit group and of prime ideals of
the field. We are investigating the practical effectiveness of GNFS.

---Dan