## A method of factoring and the factorization of $F_{7}$

HTML articles powered by AMS MathViewer

- by Michael A. Morrison and John Brillhart PDF
- Math. Comp.
**29**(1975), 183-205 Request permission

Erratum: Math. Comp.

**35**(1980), 1444.

## Abstract:

The continued fraction method for factoring integers, which was introduced by D. H. Lehmer and R. E. Powers, is discussed along with its computer implementation. The power of the method is demonstrated by the factorization of the seventh Fermat number ${F_7}$ and other large numbers of interest.## References

- John Brillhart and J. L. Selfridge,
*Some factorizations of $2^{n}\pm 1$ and related results*, Math. Comp. 21 (1967), 87-96; corrigendum, ibid.**21**(1967), 751. MR**0224532**, DOI 10.1090/S0025-5718-1967-0224532-3 - John Brillhart, D. H. Lehmer, and J. L. Selfridge,
*New primality criteria and factorizations of $2^{m}\pm 1$*, Math. Comp.**29**(1975), 620–647. MR**384673**, DOI 10.1090/S0025-5718-1975-0384673-1
D. JARDEN, - Donald E. Knuth,
*The art of computer programming. Vol. 2*, 2nd ed., Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms. MR**633878**
M. KRAITCHIK, - D. H. Lehmer,
*A Photo-Electric Number Sieve*, Amer. Math. Monthly**40**(1933), no. 7, 401–406. MR**1522863**, DOI 10.2307/2302134 - D. H. Lehmer,
*Computer technology applied to the theory of numbers*, Studies in Number Theory, Math. Assoc. America, Buffalo, N.Y.; distributed by Prentice-Hall, Englewood Cliffs, N.J., 1969, pp. 117–151. MR**0246815**
D. H. LEHMER, "An announcement concerning the delay line sieve DLS-127," - D. H. Lehmer and R. E. Powers,
*On factoring large numbers*, Bull. Amer. Math. Soc.**37**(1931), no. 10, 770–776. MR**1562254**, DOI 10.1090/S0002-9904-1931-05271-X
D. N. LEHMER, "Hunting big game in the theory of numbers," - D. N. Lehmer,
*Factor Stencils*, Carnegie Institution of Washington, Washington, 1939. Revised and extended by John D. Elder. MR**0000817** - J. C. Morehead,
*Note on Fermat’s numbers*, Bull. Amer. Math. Soc.**11**(1905), no. 10, 543–545. MR**1558255**, DOI 10.1090/S0002-9904-1905-01255-6 - Michael A. Morrison and John Brillhart,
*The factorization of $F_{7}$*, Bull. Amer. Math. Soc.**77**(1971), 264. MR**268113**, DOI 10.1090/S0002-9904-1971-12711-8
F. PROTH, - Daniel Shanks,
*Class number, a theory of factorization, and genera*, 1969 Number Theory Institute (Proc. Sympos. Pure Math., Vol. XX, State Univ. New York, Stony Brook, N.Y., 1969) Amer. Math. Soc., Providence, R.I., 1971, pp. 415–440. MR**0316385**
A. E. WESTERN, "Note on Fermat’s numbers and the converse of Fermat’s theorem,"

*Recurring Sequences*, 2nd ed., Riveon Lematematika, Jerusalem, 1966, pp. 40-59. MR

**33**#5548.

*Recherches sur la théorie des nombres*. Tome II, Gauthier-Villars, Paris, 1929. M. KRAITCHIK,

*Théorie des nombres*. Tome II, Gauthier-Villars, Paris, 1926, pp. 195-208. A. M. LEGENDRE,

*Théorie des nombres*. Tome I, 3rd ed., Paris, 1830, pp. 334-341; Also under the title,

*Zahlentheorie*, translated by H. Maser, Teubner, Leipzig, 1893, pp. 329-336.

*Math. Comp.*, v. 20, 1966, pp. 645-646.

*Scripta Math.*, 1933, pp. 229-235.

*Comptes Rendus*, Paris, v. 87, 1878, p. 374.

*Proc. London Math. Soc.*, v. 3, 1905, xxi-xxii.

## Additional Information

- © Copyright 1975 American Mathematical Society
- Journal: Math. Comp.
**29**(1975), 183-205 - MSC: Primary 10A25; Secondary 10-04
- DOI: https://doi.org/10.1090/S0025-5718-1975-0371800-5
- MathSciNet review: 0371800