E. D. F. Meissel, Berechnung der Menge von Primzahlen, welche innerhalb der ersten Milliarde naturlicher Zahlen vorkommen, Math. Ann. 25 (1885) 251-257. Home/Search Document Not in Database Summary Related Articles Check |
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Computing pi(x): The Meissel-Lehmer Method - Lagarias, Miller, Odlyzko (Correct)
....about 6p 2 (1 log 2) x nonzero terms. Actual calculations of p(x) by Gauss and others were based on factor tables made using sieve methods. The first efficient algorithm for computing p(x) which does not involve locating all the primes below x is due to the astronomer E. D. F. Meissel ( 11] [14]) His method is economical of space, and can be viewed as reducing the number of terms in Legendre s sum (1.1) Using his methods 2 he calculated p(10 8 ) 5 , 761 , 455 in 1871, and then after an enormous calculation announced in 1885 that p(10 9 ) was 50,847,478. His value of ....
E. D. F. Meissel, Berechnung der Menge von Primzahlen, welche innerhalb der ersten Milliarde naturlicher Zahlen vorkommen, Math. Ann. 25 (1885) 251-257.
Computing pi(x): The Meissel-Lehmer Method - Lagarias, Miller, Odlyzko (Correct)
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E. D. F. Meissel, Berechnung der Menge von Primzahlen, welche innerhalb des ersten Hundert Millionen naturlicher Zahlen vorkommen, Math. Ann. 3 (1871), 525-525.
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