Numbers representable by five prime squares with primes in an arithmetic progression
نویسندگان
چکیده
منابع مشابه
Gaps between Prime Numbers and Primes in Arithmetic Progressions
The equivalence of the two formulations is clear by the pigeon-hole principle. The first one is psychologically more spectacular: it emphasizes the fact that for the first time in history, one has proved an unconditional existence result for infinitely many primes p and q constrained by a binary condition q − p = h. Remarkably, this already extraordinary result was improved in spectacular fashi...
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Prime numbers have fascinated people since ancient times. Since the last century, their study has acquired importance also on account of the crucial role played by them in cryptography and other related areas. One of the problems about primes which has intrigued mathematicians is whether it is possible to have long strings of primes with the successive primes differing by a fixed number, namely...
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Abstract. Assuming the Generalized Riemann Hypothesis, we obtain a lower bound within a constant factor of the conjectured asymptotic result for the second moment for primes in an individual arithmetic progression in short intervals. Previous results were averaged over all progression of a given modulus. The method uses a short divisor sum approximation for the von Mangoldt function, together w...
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It has been a long conjecture that there are arbitrarily long arithmetic progressions of primes. As of now, the longest known progression of primes is of length 26 and was discovered by Benoat Perichon and PrimeGrid in April, 2010 ([1]): 43142746595714191+23681770·223092870n for n = 0, 1, · · · , 25. Many mathematicians have spent years trying to prove (or disprove) this conjecture, and even mo...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1999
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-90-3-217-244