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Date: 15-12-2020
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Date: 17-3-2020
887
Date: 19-9-2020
934
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The first few values are 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, ... (OEIS A001223). Rankin has shown that
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for infinitely many and for some constant (Guy 1994). At a March 2003 meeting on elementary and analytic number in Oberwolfach, Germany, Goldston and Yildirim presented an attempted proof that
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(Montgomery 2003). Unfortunately, this proof turned out to be flawed.
An integer is called a jumping champion if is the most frequently occurring difference between consecutive primes for some (Odlyzko et al.).
REFERENCES:
Bombieri, E. and Davenport, H. "Small Differences Between Prime Numbers." Proc. Roy. Soc. A 293, 1-18, 1966.
Erdős, P.; and Straus, E. G. "Remarks on the Differences Between Consecutive Primes." Elem. Math. 35, 115-118, 1980.
Guy, R. K. "Gaps between Primes. Twin Primes" and "Increasing and Decreasing Gaps." §A8 and A11 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 19-23 and 26-27, 1994.
Havil, J. Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, pp. 114-115, 2003.
Montgomery, H. "Small Gaps Between Primes." 13 Mar 2003. https://listserv.nodak.edu/scripts/wa.exe?A2=ind0303&L=nmbrthry&P=1323.
Odlyzko, A.; Rubinstein, M.; and Wolf, M. "Jumping Champions." https://www.research.att.com/~amo/doc/recent.html.
Riesel, H. "Difference Between Consecutive Primes." Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, p. 9, 1994.
Sloane, N. J. A. Sequence A001223/M0296 in "The On-Line Encyclopedia of Integer Sequences."
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تفوقت في الاختبار على الجميع.. فاكهة "خارقة" في عالم التغذية
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أمين عام أوبك: النفط الخام والغاز الطبيعي "هبة من الله"
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قسم شؤون المعارف ينظم دورة عن آليات عمل الفهارس الفنية للموسوعات والكتب لملاكاته
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