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Date: 14-2-2020
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Date: 17-11-2020
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Date: 30-5-2020
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A method for computing the prime counting function. Define the function
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(1) |
where is the floor function and the
are the binary digits (0 or 1) in
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(2) |
Legendre's formula can then be written
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(3) |
The first few values of are
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(4) |
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(5) |
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(6) |
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(7) |
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(8) |
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(9) |
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(10) |
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(11) |
Mapes' method takes time , which is slightly faster than the Lehmer-Schur method.
REFERENCES:
Mapes, D. C. "Fast Method for Computing the Number of Primes Less than a Given Limit." Math. Comput. 17, 179-185, 1963.
Riesel, H. "Mapes' Method." Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, p. 23, 1994.
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دراسة تكشف "مفاجأة" غير سارة تتعلق ببدائل السكر
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أدوات لا تتركها أبدًا في سيارتك خلال الصيف!
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العتبة العباسية المقدسة تؤكد الحاجة لفنّ الخطابة في مواجهة تأثيرات الخطابات الإعلامية المعاصرة
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