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7. References

Adleman, L. and C. Pomerance, R. Rumely, On distinguishing prime numbers from composite numbers, Ann. Math., 117 (1983) 173-206.

Agnew, J., Explorations in Number Theory, Brooks/Cole, Monterey, 1972.

Agrawal, M. and S. Biswas, Primality and identity testing via the Chinese remaindering, in 40th Ann. Symp. on Foundation of Computer Science, IEEE Computer Soc., Los Alamitos, 1999, p. 2002-208.

Agrawal, M. and N. Kayal, N. Saxena, PRIMES is in P, IIT Kanpur, Preprint of August 8, 2002. (Available on-line.)

Alford, W. and A. Granville, C. Pomerance, There are infinitely many carmichael numbers, Ann. Math., 140 (1994) 703-722.

Archibald, R., An Introduction to the Theory of Numbers, Merrill, Columbus, 1970.

Bernstein, D., Proving primality after Agrawal-Kayal-Saxena, Jan. 25, 2003. (Available on-lline.)

Bornemann, F., PRIMES Is in P: A breakthrough for "everyman," Notices of the AMS 50 (2003) 545-552.

Bressoud, D., Factorization and Primality Testing, Springer-Verlag, New York, 1989.

Burton, D., Elementary Number Theory, Allyn and Bacon, Boston, 1976.

Cohen, H. and H. Lenstra Jr., Primality testing using Jacobi sums, Math. Comp., 42 (1984) 297-330.

Cormen, T. and C. Leiserson, R. Rivest, C. Stein, Introduction to Algorithms, 2nd. edition, MIT Press, Cambridge, McGraw Hill, New York, 2001.

Dickson, L., History of the Theory of Numbers, Vol. 1-3, Chelsea Publishing, New York, 1952. (Chelsea Books are now distributed by the American Mathematical Society, Providence.)

Diffie, W. and M. Hellman, New directions in cryptography, IEEE Trans. Inform. Theory, 22 (1976) 472-492.

Dudley, U., History of a formula for primes, Amer. Math. Monthly, 76 (1969) 23-28.

Dudley, U., Formulas for primes, Math. Mag., 56 (1983) 17-22.

Dudley, U., Elementary Number Theory, 2nd. ed., W. H. Freeman, San Francisco, 1978.

Erdös, P. and C. Pomerance, On the number of false witnesses for a composite number, Math. Comp., 46 (1986) 259-279.

Goldman, J., The Queen of Mathematics: A Historically Motivated Guide to Number Theory, A.K. Peters, Wellesley, 1998.

Hall. T., Carl Friedrich Gauss: A Biography, A. Froderberg, translator, MIT Press, Cambridge, 1990.

Ingham, A., The Distribution of Prime Numbers, Cambridge U. Press, Cambridge, 1932.

James, I., Remarkable Mathematicians, Cambridge U. Press, Cambridge, MAA, Washington, 2002.

Kaufmann-Bühler, W., Gauss: A Biographical Study, Springer-Verlag, New York, 1981.

Long, C., Elementary Introduction to Number Theory, Heath, Boston, 1965.

Merkle, R., Secrecy, authentication, and public key systems, Ph.D., Dept. Electrical Engineering, Stanford Univ., 1979.

Miller, G., Riemann's hypothesis and tests for primality, J. of Computer and Systems Sciences, 13 (1976) 300-317.

Mollin, R., An Introduction to Cryptography, Chapman & Hall/CRC Press, Boca Raton, 2001.

Mollin, R., RSA and Public-Key Cryptography, CRC Press, Boca Raton, 2003

Niven, I. and H. Zuckerman, An Introduction to the Theory of Numbers, Wiley, New York, 1960.

Pollard, J., Theorems on factorization and primality testing, Pro. Camb. Phil. Soc., 76 (1974) 521-528.

Rabin, M., Probabilistic algorithm for testing primality, J. of Number Theory, 12 (1980) 128-138.

Rademacher, H., Lectures on Elementary Number Theory, Blaisdall, New York, 1964.

Ribenboim, P., The book of prime number records, Springer-Verlag, New York, 1989.

Ribenboim, P., The Little Book of Big Primes, Springer-Verlag, New York, 1991.

Rittaud, B., 31415879 Ce nombre est-il premier?, La Recherche, Mensuel 361, Février, 2003, p. 70-73.

Rivest, R. and A. Shamir, L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Comm. ACM., 21 (1978) 120-126.

Rosen, K., (ed.), Handbook of Discrete and Combinatorial Mathematics, CRC Press, Boca Raton, 2000.

Rosen, K., Discrete Mathematics and its Applications, Fifth Edition, McGraw Hill, New York, 2003.

Stinson, D., Cryptography, CRC Press, Boca Raton, 2002.

Tattersall, J., Elementary Number Theory in Nine Chapters, Cambridge U. Press, Cambridge, 1999.

Wagstaff, S., Cryptanalysis of Number Theoretic Ciphers, CRC Press, Boca Raton, 2003.

Washington, L., Elliptic Curves, Number Theory and Cryptography, CRC Press, Boca Raton, 2003.

Weill, A., Number Theory: An Approach through History from Hammurapi to Legendre, Birkhäuser, Boston, 1984.

Those who can access JSTOR can find some of the papers mentioned above there.

  1. Introduction
  2. Basic Ideas
  3. Distribution of the primes
  4. Complexity and algorithms
  5. Primes and cryptography
  6. The right stuff
  7. References