70-million Bounded Gap Between Primes

Since Ancient Greek :

  1. Euclid had proved there are infinite primes.
  2. Sieve of Eratosthenes to enumerate the primes.
  3. Recent time 3 Mathematicians GPY attempted another Sieve method to find the bounded gap (N) of primes in infinity, but stuck at one critical step.
  4. Dr. YiTang Zhang 张益唐 (1955 -) spent 7 years in solitude after failure in academic career, in 2013 during a 10-min walk at the deer backyard of his friend’s house, he found an Eureka solution for the GPY’s critical step: \boxed { \epsilon = \frac {1} {168}} which gave the first historical bounded Gap (N) from an infinity large number to a limit of 70 million.


  • Chinese love the number “8” \ba which sounds like the word prosperity 发 \fa (in Cantonese) . He could have instead used 160, so long as \epsilon is small.
  • The Ultimate Goal of the Bounded Gap (N) is 2 (Twin Primes Conjecture) .
  • The latest bounded gap (N) is reduced from 70-million to 246 from The PolyMath Project led by Terence Tao using Zhang’s method by adjusting the various values of \epsilon (analogous to choosing different sizes of the holes or ‘eyes’ of the Prime Sieve.)

A Graduate Level Talk by Dr. Zhang:

A Simpler Overview:


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