Zobrazeno 1 - 10 of 131 pro vyhledávání: '"Prime quadruplet"'
1
Twin primes and the parity problem
Autor: Akshaa Vatwani, M. Ram Murty
Publikováno v: Journal of Number Theory. 180:643-659
We formulate a conjecture regarding the equidistribution of the Mobius function over shifted primes in arithmetic progressions. Our main result is that such a conjecture for a fixed even integer h, in conjunction with the Elliott–Halberstam conject
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d23d24591d68f5c5de4efcf66d130a3f
https://doi.org/10.1016/j.jnt.2017.05.011
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2
Goldbach–Linnik type problems with unequal powers of primes
Autor: Zhixin Liu
Publikováno v: Journal of Number Theory. 176:439-448
In this short paper, it is proved that every sufficiently large even integer is a sum of two squares of primes, two cubes of primes, two fourth powers of primes and 41 powers of 2. Furthermore, there are at least 3.682% odd integers that can be repre
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::8a0852f47a3a76f19a304546806cb202
https://doi.org/10.1016/j.jnt.2016.12.009
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3
Bounded gaps between Gaussian primes
Autor: Akshaa Vatwani
Publikováno v: Journal of Number Theory. 171:449-473
We show that there are infinitely many distinct rational primes of the form p 1 = a 2 + b 2 and p 2 = a 2 + ( b + h ) 2 , with a , b , h integers, such that | h | ≤ 246 . We do this by viewing a Gaussian prime c + d i as a lattice point ( c , d ) i
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::bd94a42b0895bcfeb3527f8c9c74e1f6
https://doi.org/10.1016/j.jnt.2016.07.008
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5
On the largest prime factor of shifted primes
Autor: Feng Juan Chen, Yong Gao Chen
Publikováno v: Acta Mathematica Sinica, English Series. 33:377-382
For any integer n ≥ 2, let P(n) be the largest prime factor of n. In this paper, we prove that the number of primes p ≤ x with P(p−1) ≥ p c is more than (1−c+o(1))π(x) for 0 < c < 1/2. This extends a recent result of Luca, Menares and Mada
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d55361680a6d0e9b1c7a03e69f478c4d
https://doi.org/10.1007/s10114-016-5121-3
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6
Some properties of elements of the prime field
Autor: S. A. Tyurin
Publikováno v: Russian Mathematics. 60:52-59
We obtain some properties of primitive roots in the groups of residue class modulo prime number, in particular, Fermat primes and Sophie Germain primes. We also obtain some formulas for computation of products of elements in some subsets of the prime
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::c3efe3758660e4b337b2d0bb4194d762
https://doi.org/10.3103/s1066369x16080065
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8
On a conjecture of de Koninck
Autor: Xin Tong, Yong-Gao Chen
Publikováno v: Journal of Number Theory. 154:324-364
For a positive integer n, let σ(n) and γ(n) denote the sum of divisors and the product of distinct prime divisors of n, respectively. It is known that, if σ(n)=γ(n)2, then at most two exponents of odd primes are equal to 1 in the prime factorizat
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::c9aa7a0e65bbf40e275d945ec11d8ce4
https://doi.org/10.1016/j.jnt.2015.02.004
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9
On the number of strong primes
Autor: X. M. Meng
Publikováno v: Acta Mathematica Hungarica. 145:505-515
A prime number p is called strong if p − 1 and p + 1 each have a large prime factor. Let x be a large positive number. We show a lower bound on the number of strong primes p between 1 and x such that p−1 and p+1 each have a prime factor larger th
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::bec866b30fe253b390b70ad9d88733b8
https://doi.org/10.1007/s10474-015-0489-6
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