Problems & Puzzles: Problems

Problem 15.- Why the Twin Constant is so close to 2/3?

Marek Wolf (17/11/98) has proposed the following problem:

"Is there any (heuristic) reason why the value of the twin constant C2=0.66016... is so close to 2/3?"

C2 is called the "twin prime constant" and is the infinite product:

C2 = Product {1 – 1/(p-1)2 }, for p>2.

Wrench calculated first this constant in 1961.

A modern value is this:

0.660161815846869573927812110014555778432623360…

See:

  1. Ref. 1, p. 262
  2. http://www.utm.edu/research/primes/glossary/TwinPrimeConstant.html
  3. http://www.lacim.uqam.ca/pi/table.html

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