Some results on pseudosquares

@article{Lukes1996SomeRO,
  title={Some results on pseudosquares},
  author={Richard F. Lukes and C. D. Patterson and Hugh C. Williams},
  journal={Math. Comput.},
  year={1996},
  volume={65},
  pages={361-372}
}
If p is an odd prime, the pseudosquare Lp is defined to be the least positive nonsquare integer such that Lp ≡ 1 (mod 8) and the Legendre symbol (Lp/q) = 1 for all odd primes q ≤ p. In this paper we first discuss the connection between pseudosquares and primality testing. We then describe a new numerical sieving device which was used to extend the table of known pseudosquares up to L271. We also present several numerical results concerning the growth rate of the pseudosquares, results which so… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 13 references

Quadratic residues in factorization

M. Hall
Bull. Amer. Math. Soc • 1933
View 6 Excerpts
Highly Influenced

An open architecture number sieve

A. J. Stephens, H. C. Williams
Number Theory and Cryptography (Sydney, • 1989
View 11 Excerpts
Highly Influenced

Integer sequences having prescribed quadratic character

D. H. Lehmer, E. Lehmer, D. Shanks
Math. Comp • 1970
View 4 Excerpts
Highly Influenced

Lehmer, A fallacious principle in the theory of numbers

D H.
Bull. Amer. Math. Soc • 1930
View 4 Excerpts
Highly Influenced

Congruential sieves on FPGA computers

N. D. Bronson, D. A. Buell
Proc. Sympos. Appl. Math., vol • 1994
View 2 Excerpts

Primality testing and Abelian varieties over finite fields

L. M. Adleman, M.-D. Huang
Lecture Notes in Math., • 1992
View 2 Excerpts

A 538 billion integer per second sieve

C. Patterson
Proc. 1991 Canad. Conf. on Electrical and Computer Engineering, • 1991
View 2 Excerpts

On Primality Tests

SIAM J. Comput. • 1982
View 1 Excerpt

Primality testing on a computer

H. C. Williams
Ars Combin • 1978
View 2 Excerpts

Similar Papers

Loading similar papers…