There are 105212 Carmichael numbers up to 10^{15}: we describe
the calculations. The numbers were generated by a back-tracking search for
possible prime factorisations, and the computations checked by
searching selected ranges of integers directly using a sieving technique,
together with a ``large prime variation''.

See the full paper in PS format.

Zbl. 780.11069

Math Review 93m:11137

Arxiv:math.NT/9803082 or here.

See the full paper in PS format.

See the full paper in DVI or PS format.

See the full paper in PS format.

See a poster for the ANTS VII meeting in PS format.

We further extend our computations to show that there are
20138200 Carmichael numbers up to 10^{21}.

See a poster for the ANTS VIII meeting in PDF format.

See the the full paper in PDF format.

`carmichael-16.gz`

All Carmichael numbers up to 10^{16}in GZIP format`carmichael17.gz`

All Carmichael numbers between 10^{16}and 10^{17}in GZIP format`carmichael18.gz`

All Carmichael numbers between 10^{17}and 10^{18}in GZIP format`car3-18.gz`

All Carmichael numbers with 3 prime factors up to 10^{18}in GZIP format- Counts by powers of 10 and number of prime factors, together with the smallest Carmichael numbers with k prime factors and other statistics.

Proceedings 6th
IMA
Conference on Coding and Cryptography, Cirencester 1997, (ed. M. Darnell)
Springer Lecture Notes in Computer Science
**1355** (1997) 265--269

We show that the inadvertent use of a Carmichael number instead of a prime factor in the modulus of an RSA cryptosystem is likely to make the system fatally vulnerable, but that such numbers may be detected.

See the paper in DVI or PS format.

4th International Algorithmic Number Theory Symposium,
ANTS-IV, Leiden,
The Netherlands, 2--7 July 2000;
Springer Lecture Notes in Computer Science
**1838** (2000), 459-474

There are 38975 Fermat pseudoprimes (base 2) up to 10^{11}, 101629 up
to 10^{12} and 264239 up to 10^{13}:
we describe the calculations and give some statistics.
The numbers were generated by a variety of strategies, the
most important being a back-tracking search for possible prime
factorisations, and the computations checked by a sieving technique..

See the full paper in PDF format. (Copyright © Springer-Verlag 2000)

`psp-12.gz`

The 101629 pseudoprimes up to 10^{12}in GZIP format`psp13.gz`

The 162610 pseudoprimes between 10^{12}and 10^{13}in GZIP format`spsp-13.gz`

The 58892 strong (Miller--Rabin) pseudoprimes up to 10^{13}in GZIP format`even-12`

The 155 even pseudoprimes up to 10^{12}.

Some preprints are available in the Number Theory section of the eprint Arxiv: try here or use the UK mirror site at Southampton

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Updated 24/03/2008 by Richard Pinch