Factoring: Most Wanted List

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Robert D. Silverman

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May 22, 1986, 10:03:42 PM5/22/86
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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.

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