Problem 54755. List odd twin composites
Twin primes, or prime numbers that differ by 2 (e.g., 17 and 19, 59 and 61, or 191 and 193), are the subject of several Cody problems: 248, 1096, 3016, and 52298. (See also Cody Problem 53740 for “almost twin primes”.)
This problem deals with twin composites. Because all even numbers are twin composites, let’s focus on odd twin composites, such as 25 and 27, 63 and 65, and 169 and 171.
Write a function that takes a number and produces a two-column matrix with the smaller number of the odd twin composite pair in the first column and the larger in the second column.
Optional exercises: (a) prove that the number of odd twin composites is infinite, (b) prove that the number of twin primes is infinite.
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Prime Numbers III
- 19 Problems
- 4 Finishers
- List the Moran numbers
- List the cuban primes
- Compute the largest number whose prime factors sum to n
- List the Beatriz numbers
- List the Euclid numbers
- List odd twin composites
- List the semiprimes
- Solve an equation involving primes and fractions
- List the two-bit primes
- List numbers such that every sum of consecutive positive integers ending in those numbers is composite
- Identify de Polignac numbers
- List the Fermi-Dirac primes
- Factor a number into Fermi-Dirac primes
- Compute the Sisyphus sequence
- Compute the bubble popper fidget spinner sequence
- Determine whether a number is a Zeisel number
- Express numbers as the sum of a prime, a square, and a cube
- Determine whether a number is a Gaussian prime
- List primes of the form xy+z
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