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. -------------------------------------------------------------- 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.