/jac-3

Attempt to find counterexample for jac-3 conjecture

Primary LanguageRust

#Purpose This project is written to gather information on the following conjecture: All jac-3 numbers have at least one prime factor of 3

#Definitions

  • Digit frequencies : the number of times each digit occurs in the base 10 representation of the number; "25" -> { 2: 1, 5: 1 }
  • Jac number : a number whos digit frequencies match the digit frequencies of its prime factors. To combine the digit frequencies of the factors, take an elementwise sum; ex: 4 has { 4: 1 }, prime factor is 2 2 so combine digit frequencies is { 2: 2 }; {4: 1} != {2: 2}
  • Jac-3 : a jac number which has precisely 3 prime factors; ex: 2 * 2 * 2 = 8 or 2 * 3 * 5 = 30 (these are not jac numbers)

#Conjecture All jac-3 numbers have at least one prime factor of 3. If 2 * 3 * 5 is a jac number, it is also a jac-3, and agrees with the conjecture that all jac-3's have a prime factor of 3

Actual Jac-3 numbers

| Num | Factors | | 1353669 | 3, 653, 691 |