Largest Known Twin Prime Pair
On January 15, 2007 two distributed computing projects, Twin Prime Search and PrimeGrid found the largest known twin primes, 2003663613 · 2195000 ± 1. The numbers have 58711 decimal digits. Their discoverer was Eric Vautier of France.
On August 6, 2009 those same two projects announced that a new record twin prime had been found. It is 65516468355 · 2333333 ± 1. The numbers have 100355 decimal digits.
On December 25, 2011 PrimeGrid announced that yet another record twin prime had been found. It is 3756801695685 · 2666669 ± 1. The numbers have 200700 decimal digits.
An empirical analysis of all prime pairs up to 4.35 · 1015 shows that if the number of such pairs less than x is f(x)·x/(log x)2 then f(x) is about 1.7 for small x and decreases towards about 1.3 as x tends to infinity.
There are 808,675,888,577,436 twin prime pairs below 1018.
The limiting value of f(x) is conjectured to equal twice the twin prime constant (not to be confused with Brun's constant)
(sequence A114907 in OEIS) this conjecture would imply the twin prime conjecture, but remains unresolved.
The twin prime conjecture would give a better approximation, as with the prime counting function, by
Read more about this topic: Twin Prime
Famous quotes containing the words largest, twin, prime and/or pair:
“The largest pond is as sensitive to atmospheric changes as the globule of mercury in its tube.”
—Henry David Thoreau (1817–1862)
“That Dali is really Norman Rockwell’s twin brother kidnapped by gypsies in babyhood.”
—Vladimir Nabokov (1899–1977)
“By whatever means it is accomplished, the prime business of a play is to arouse the passions of its audience so that by the route of passion may be opened up new relationships between a man and men, and between men and Man. Drama is akin to the other inventions of man in that it ought to help us to know more, and not merely to spend our feelings.”
—Arthur Miller (b. 1915)
“You are always looking for already-felt emotions, just as you like to get an old pair of trousers back from the cleaners, which seem new when you don’t look too closely. Artists are cleaners, don’t let yourself be taken in by them. True modern works of art are made not by artists but quite simply by men.”
—Francis Picabia (1878–1953)