— Function: primep number &optional certainty-threshold

Return nil if number is known to be composite, return t if number is definitely prime and return 'probably-prime if number seems to be prime but it is not certain.

If optional argument certainty-threshold is non-nil, it should be a natural number to indicate how many probabilistic primality tests must be passed in order to have certainty about the primality of number. The default is 8.

— Function: next-prime number

Return the next prime number greater than number.

— Function: gcd &rest numbers

Return the greatest common divisor of the arguments.

— Function: xgcd &rest numbers

— Function: lcm &rest numbers

Return the least common multiple of the arguments.

— Function: factorial number

Return the factorial of number.

— Function: binomial-coefficient n k

Return the binomial coefficient, n over k.

— Function: fibonacci number

Return the numberth Fibonacci number. To compute both, the numberth and (number-1)th Fibonacci number use fibonacci2 instead.

— Function: fibonacci2 number

Return a cons with the numberth and (number-1)th Fibonacci number. To compute a series of Fibonacci numbers starting at index number, use this function and recursively compute the rest.

— Function: lucas number

Return the numberth Lucas number. To compute both, the numberth and (number-1)th Lucas number use lucas2 instead.

— Function: lucas2 number

Return a cons with the numberth and (number-1)th Lucas number. To compute a series of Lucas numbers starting at index number, use this function and recursively compute the rest.

— Function: divisiblep number d

Return t if number is divisible by d, nil otherwise.

— Function: congruentp number c m

Return t if number is congruent to c modulo m, nil otherwise.

— Function: perfect-power-p number

Return t if number is a perfect power, nil otherwise. An integer number is said to be a perfect power if there exist integers, a and b, such that ‘a^b = number’.

— Function: perfect-square-p number

Return t if number is a perfect square, nil otherwise. An integer number is said to be a perfect square if there exists an integer b such that ‘b^2 = number’.

— Function: integral-sqrt number

Return a cons with the integral square root of number in the car and the remainder in the cdr. An integral square root is a number b and a remainder c such that ‘b*b + c = number’.

— Function: canonical-norm number

Return the canonical norm of number.

— Function: conjugate number

Return the (canonical) conjugate of number. If number is a comparable, just return number.

— Function: zero-divisor-p number

Return t if number is a zero-divisor, nil otherwise. number is said to be a zero-divisor, if there exists another non-zero number b, such that ‘number * b = 0’

— Function: unitp number

Return t if number is a unit, nil otherwise. number is said to be a unit, if there exists another number b (the inverse of number), such that ‘number * b = 1’