Factorial primes are of interest to number theorists because they sometimes signal the end or the beginning of an extraordinarily lengthy run of consecutive composite numbers. For example, the prime following 479,001,599 is 479,001,629.
For a long time, prime numbers were thought as having no possible application outside of number theory; this changed in the 1970s when the concepts of public-key cryptography were invented, in which prime numbers formed the basis of the first algorithms such as the RSA cryptosystem or the Diffie-Hellman key-exchange algorithm.
A probable prime is an integer which, by virtue of having passed a certain test, is considered to be probably prime.
With this definition, the primes of the field Q of rational numbers are represented by the standard absolute value function (known as the "infinite prime") as well as by the p-adic valuations on Q, for every prime number p.
Feeds |
Contact