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where f (2k−1) is the (2k − 1)th derivative of f and B 2k is the (2k)th Bernoulli number: B 2 = 1 / 6 , B 4 = − + 1 / 30 , and so on. Setting f ( x ) = x , the first derivative of f is 1, and every other term vanishes, so [ 15 ]
As of September 2015, the largest confirmed Lucas prime is L 148091, which has 30950 decimal digits. [4] As of August 2022, the largest known Lucas probable prime is L 5466311, with 1,142,392 decimal digits. [5] If L n is prime then n is 0, prime, or a power of 2. [6] L 2 m is prime for m = 1, 2, 3, and 4 and no other known values of m.
[2] [3] Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics , most notably in Euclid 's Elements . [ 4 ] Since its beginning, mathematics was primarily divided into geometry and arithmetic (the manipulation of natural numbers and fractions ), until the 16th and 17th centuries, when ...
2 4, a time signature in music; 2×4 (Guadalcanal Diary album), 1987; 2×4 (Einstürzende Neubauten album), 1984; 2×4 (Malachi Favors and Tatsu Aoki album), 1999; Two by Four, 1989 album by Marc Johnson "2×4", a 1996 song by Metallica from their album Load "2×4", a 1995 song by Blind Melon from their album Soup