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Date: 6-4-2020
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Date: 23-8-2020
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Date: 2-11-2019
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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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دراسة يابانية لتقليل مخاطر أمراض المواليد منخفضي الوزن
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اكتشاف أكبر مرجان في العالم قبالة سواحل جزر سليمان
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اتحاد كليات الطب الملكية البريطانية يشيد بالمستوى العلمي لطلبة جامعة العميد وبيئتها التعليمية
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