Corrections to "The Joy of Factoring" published in 2013
Page 58. Change "M" to "m" twice in Example 3.25.
Page 79. Change "Theorem 4.1 with p" to "Theorem 4.1 with b"
in Examples 4.2 and 4.3.
Page 115. The second sentence after the quotation is false.
The two numbers Davis and Holdridge factored were the last two
Mersenne numbers considered by Mersenne in 1644. The last
numbers considered in the 1925 Cunningham-Woodall book were
factored in 1992.
Page 132. Theorem 5.20 needs the additional hypothesis that
a and b are positive. When one of a, b is negative, the
factorization of N might be trivial, as shown by the example
a = 1, b = -2, x = 63, y = 31, u = 65, v = 9.
Page 140. Change "Zimmerman" to "Zimmermann". Also on Page 140,
Vang was the sole discoverer of the 54-digit factor. Zimmermann
and Kruppa are listed because they wrote parts of the ECM program
he used.
Page 159. In the product at the bottom of the page, the subscript
on p should be j, not i.
Page 166, line 1. Change "F^{-1/2}" to "F_{52}^{-1/2}".
Page 167, Algorithm 6.25. The variable i in the while loop might
be off by 1, that is, maybe the loop should begin with i = 2.
Page 169, lines 6,7: This sentence is false. Pell's equation
has nothing to do with Pell or Rahn. The Bohemian mathematician
Franz von Schafgotsch [ Abhandlung \"uber einige Eigenschaften
der Prim- und zusammengesestzten Zahlen, Abhandlung der
B\"ohmischen Gesellschaft der Wissenschaften in Prag, (1786),
123--159 ] factored N = 909191 by solving the Pell equation
x^2 - 5Ny^2 = 1 . The fundamental solution is
79048274170565173862934965626849290055118667858724583379760874^2 =
5N * 37074886179336725828048723088160784804513634289660763498655^2 + 1 .
He then determines the gcd of
79048274170565173862934965626849290055118667858724583379760874 + 1
and 5N = 4545955 to find the factorization
909191 = 263 * 3457.
I am grateful to Prof. Dr. Franz Lemmermeyer for this correction.
Page 181, line -16. Add "fails" after "The p - 1 Method".
Page 186. Change "Zimmerman" to "Zimmermann".
Page 246, Section 10.3. In fact there are several phone apps
for factoring large integers.
Page 246, footnote 3. Change "declension" to "conjugation".
Also, googlare is an Italian verb, too.
Page 264, line 2. Change "the QS" to "QS".
Page 265, line -4. kR should not equal a square, that is, we
want 0 < |kR - m^2| < 1.
Page 270. Change "even" to "odd" in the answer for exercise 2.3.
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News:
A couple of days after this book went to press in September,
2013, Ryan Propper set a new record for largest prime factor
discovered by the Elliptic Curve Method. He found an 83-digit
prime factor of the Cunningham number 7,337+ c237. The remarks
about ECM records on page 186 should be updated.
According to the table on page 262, by 1995 the Fermat numbers
through F_11 had been completely factored. In the next year,
when Richard Guy was 80 years old and writing a book with John
Conway, Richard bet John that at least one more Fermat number
would be completely factored during the next twenty years, that
is, by Richard's 100-th birthday in 2016. Although he lost
the bet, Richard appeals to all factorers to try to finish F_12,
F_13, or any larger Fermat number. The comments at the top of
page 263 tell how you can help.