It is very significant! Especially when looking at the Twin Prime Conjecture
Statement 1: There are an infinite amount of primenumbers (Euclid's theorem)
Statement 2: There are an infinite amount of prime pairs for any possible finite gap (Polignac's conjecture)
Statement 3: No matter the size of the primenumber, there will always be prime with a gap less then 70 million ( 7 x 10^7) By Zhang Yitang
When looking at twin-pairs:
- Distance 2: 29-31, 101-103.. but also 3756801695685 · 2666669 ± 1 (200700 digits!!)
- Distance 6 (sexy primes): 5-11, 251-257 etc (largest know is 11 thousand digits!)
Now the significant part of the discovery.. Zhang has proof that no matter the size of the prime (thousands of digits), there will always be primes with a gap les then 70 million (only 8 digits); this was before him never proved or disproved.
What does this mean for PrimeGrid? That twin-prime-search (gap=2) could go on in larger regions (higher K's) and still be able to find twin-prime... or search for cousin primes (gap=4), or sexy primes (gap=6).
So keep searching.. and you shall keep finding twin-primes with gaps below 70million!
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