Twin Prime Conjecture

Conjecture

It is conjectured that there exist infinitely many pairs of twin primes: that is, primes which differ by $2$.


Hilbert $23$

This problem is no. $8c$ in the Hilbert $23$.


Landau's Problems

This is the $2$nd of Landau's problems.


Sources

  • 1979: G.H. Hardy and E.M. Wright: An Introduction to the Theory of Numbers (5th ed.) ... (previous) ... (next): $\text I$: The Series of Primes: $1.4$ The sequence of primes
  • 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $1,32032 36316 \ldots$
  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1 \cdotp 90195 \ldots$
  • 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): twin primes
  • 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.16$: The Sequence of Primes
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1 \cdotp 90216 \, 054 \ldots$
  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): twin primes (prime pair)
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): twin primes (prime pair)
  • 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $7$: Patterns in Numbers: Fermat
  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): twin primes
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