chibi-math

Returns true if we can show n to be composite using the Miller-Rabin test (i.e., finding a witness a where a^(n-1)≠1 mod n or a reveals the existence of a 3rd square root of 1 in Z/(n))

`probable-prime?`

[procedure] (probable-prime? n)

Returns true if n has a very high probability (enough that you can assume a false positive will never occur in your lifetime) of being prime.

`prime?`

[procedure] (prime? n)

Returns true iff n is prime. Uses provable-prime? for small n, falling back on probable-prime? for large values.

Prime iteration and factorization

`nth-prime`

[procedure] (nth-prime i)

Returns the nth prime, with 2 being the 0th prime.

`prime-below`

[procedure] (prime-below n)

Returns the first prime less than or equal to n, or #f if there are no such primes.

`prime-above`

[procedure] (prime-above n #!optional (limit #f))

Returns the first prime greater than or equal to n. If the optional limit is given and not false, returns #f if no such primes exist below limit.

`factor-alist`

[constant] factor-alist

Returns the factorization of n as a list of elements of the form (p . k)}, where {{p is a prime factor and k is its multiplicity.

`factor`

[constant] factor

Returns the factorization of n as a monotonically increasing list of primes.

`totient`

[constant] totient

The Euler totient φ(n) is the number of positive integers less than or equal to n that are relatively prime to n.

`aliquot`

[constant] aliquot

The aliquot sum s(n) is the sum of proper divisors of a positive integer n.

`perfect?`

[procedure] (perfect? n)

Returns true iff n is a perfect number, i.e. the sum of its divisors other than itself equals itself.

Random prime generation

`random-prime`

[procedure] (random-prime lo hi)

Returns a random prime between lo, inclusive, and hi, exclusive.

`random-prime-distinct-from`

[procedure] (random-prime-distinct-from lo hi p)

Variant of random-prime which ensures the result is distinct from p.

`random-coprime`

[procedure] (random-coprime n)

Returns a random integer less than n relatively prime to n.

Maintainer

Diego A. Mundo

Author

Alex Shinn

Version History

0.1.0

License

BSD

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