bs@faron.UUCP (Robert D. Silverman) (05/23/86)
While I continue the process of factoring numbers on the current 'WANTED'
lists I encountered a very rare and unusual event: A very large number
which factored as the product of two VERY nearly equal primes. The
factorization was that of a 77 digit cofactor of 6^106 + 1. This number
has the trivial algebraic factor 37, and a small primitive factor 26713.
The remain cofactor, however, factors as:
175436926004647658810244613736479118917 *
175787157418305877173455355755546870641
A very pretty result.
It not only is unusual for a number this size to factor into two primes
of equal length but also it is even more unusual that the first 3 digits
are the same. Note that this is not an artificially constructed RSA key.
Bob Silverman
P.S. For those interested the current numbers left on the 'MOST WANTED'
list are: (Cxx indicates a composite number of xx digits)
512
1. 2 + 1 = 2424833.C148
128
2. 5 + 1 = 2.257.C87
128
3. 7 + 1 = 2.257.769.197231873.C95
4. finished
5. finished
6. finished
94
7. 10 + 1 = 101.45121.C88
97
8. 10 - 1 = 3.3.12004721.C89
97
9. 10 + 1 = 11.C96
10. finished
Is anyone out there bold enough to try these?????
We are waiting for John Selfridge to draw up a new list.