![]() ![]() He has now extended his enumeration of twin primes and the sum of their reciprocals to 3.155 x 10 15, having found 3,471,427,262,962 twin primes. One of these projects was initiated in 1993 by Thomas R. In recent years, twin primes and Brun’s constant have been the focus of several massive computing efforts. ![]() The fact that this sum converges demonstrates that twin primes are relatively scarce–even though there may be infinitely many of them! In contrast, the sum of the reciprocals of all primes diverges. ![]() In 1919, Norwegian mathematician Viggo Brun (1885–1978) proved that if you add together the reciprocals of successive twin primes, the sum converges to a specific numerical value now called Brun’s constant. It was even mentioned in the 1996 movie A Mirror Has Two Faces, which starred Barbra Streisand. Indeed, the twin prime conjecture is considered one of the major unsolved problems in number theory. Although most mathematicians believe that there are infinitely many twin primes, no one has yet proved this conjecture to be true. ![]()
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