Ken's blog

B different balls in an urn.  uniformly draw with replacement N times.  what is the probability that all B balls are seen during the N draws...

4 consecutive primes as near to each other as they can possibly be is called a prime 4-tuplet or prime quadruplet or prime decade because, f...

we set up some common chess openings, direct one side to play the worst moves according to MultiPV of the Stockfish chess engine and the oth...

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

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...

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), (...

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

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...

Pennsylvania has a very large number of municipalities (2560), with many duplicated and similar names.  we work with this spreadsheet https:...

primitive binary trinomials , i.e., primitive polynomials over the field GF(2) with three terms including a nonzero constant term (i.e., 1),...