Ken's blog

unicursal labyrinth: 2 endpoints and a path between them.  lots of twists and turns but no branches.  perhaps a meditation exercise, perhaps...

odd numbers have multiplicative inverses modulo 2^n (even numbers do not). ? for(n=1, 8, print1(2^n,":"); for(j=1, 2^(n-1), i=2*j...

a multiplication table between pairs of small prime numbers: * 13 17 19 23 29 31 37 41 ...

start with a set of consecutive primes.  compute all pairs positive differences among the set, and count the number of times each difference...

on a modern computer, Pari/GP can usually factor RSA-style numbers (the worst case for factoring) of 60 digits (199 bits) in 30 seconds or l...

roll some dice, order them by some metric independent of what number the die shows, then read off the numbers in that order. example dice ...

below are some numbers N with many divisors and for which N-1 and N+1 are both prime, i.e., twin primes. the suffix A indicates a highly c...

200 bit: mean= 534 ms, std= 1062 ms, n= 10000 201 bit: mean= 564 ms, std= 1112 ms, n= 10000 202 bit: mean= 599 ms, std= 1186 ms, n= 10000 ...

IEEE 754 floating point can represent infinities and Not a Number without crashing (in contrast to integers, which cannot represent those): ...

below are the 73 twin primes of the form (2^a * 3^b plus and minus 1) less than 2^10000 ~= 10^3010. (2^2 * 3^0 +- 1), (2^1 * 3^1 +- 1), (...

we permute the numbers 1..n using the randomness of the prime numbers. there are many ways to do this.  we implement the "inside-out...

collisions in hash functions are unavoidable.  if you find one collision (messages A and B have the same hash), how easy is it to manufactur...

obtaining a whole bunch of regular dice (d6) and rolling them simultaneously seems not very difficult.  (Amazon currently sells sets of as m...

each composite number below consists of repetitions of the digit string 1234567890 except the final few digits.  the smaller factors are lar...

below is Pari/GP code which prints out a table for the optimal amount of trial division to do before calling ispseudoprime on large primes, ...

given a group of people armed with paper and pencils, what size number can they (probably) prime factor in a given amount of time?  what alg...

define an RSA number to be a number that factors into exactly two prime numbers, the larger being less than twice the smaller. isrsa(n)=my...

finite differences are a common way to analyze sequences of numbers.  we compute first, second,... twentieth differences of prime numbers in...