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Date: 30-6-2020
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Date: 25-11-2020
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Date: 11-10-2020
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The next prime function gives the smallest prime larger than . The function can be given explicitly as
where is the th prime and is the prime counting function. For , 2, ... the values are 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13, 13, 17, 17, 17, 17, 19, ... (OEIS A007918).
The next prime function is implemented in the Wolfram Language as NextPrime[n].
Finding the next prime after gives the smallest -digit prime. For , 2, ..., the first few of these are 2, 11, 101, 1009, 10007, 100003, 1000003, ... (OEIS A003617). The amounts by which these exceed are 1, 1, 1, 9, 7, 3, 3, 19, 7, 7, ... (OEIS A033873).
REFERENCES:
O'Hara, F. "The Smallest and Largest -Digit Primes for ." J. Recr. Math. 22, No. 4, 277-279, 1990.
Sloane, N. J. A. Sequences A003617/M2008, A007918, and A033873 in "The On-Line Encyclopedia of Integer Sequences."
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مخاطر خفية لمكون شائع في مشروبات الطاقة والمكملات الغذائية
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"آبل" تشغّل نظامها الجديد للذكاء الاصطناعي على أجهزتها
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المجمع العلميّ يُواصل عقد جلسات تعليميّة في فنون الإقراء لطلبة العلوم الدينيّة في النجف الأشرف
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