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:
“Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.”
—Pierre Simon De Laplace (1749–1827)
“If they be two, they are two so
As stiff twin compasses are two;
Thy soul, the fixed foot, makes no show
To move, but doth if th’ other do.”
—John Donne (1572–1631)
“I came there as prime steak and now I feel like low-grade hamburger.”
—Joycelyn Elders (b. 1933)
“Here comes a pair of very strange beasts, which in all
tongues are called fools.”
—William Shakespeare (1564–1616)