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THERE ARE INFINITELY MANY PRIME NUMBERS
"... There are numerous proofs that there are infinitely many primes. Several of the nicest proofs appear in [1]. We give another. Suppose there are finitely many odd primes, p1 < · · · < pk. Then every odd number can be written in the form p α1 1 However, suppose p α1 1 · · · pαk k. · · · pα ..."
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There are numerous proofs that there are infinitely many primes. Several of the nicest proofs appear in [1]. We give another. Suppose there are finitely many odd primes, p1 < · · · < pk. Then every odd number can be written in the form p α1 1 However, suppose p α1 1 · · · pαk k
On Functions Satisfying Modular Equations for Infinitely Many Primes
"... In this paper we study properties of the functions which satisfy modular equations for infinitely many primes. The two main results are: 1) every such function is analytic in the upper half plane; 2) if such function takes the same value in two different points z 1 and z 2 then there exist an fpres ..."
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In this paper we study properties of the functions which satisfy modular equations for infinitely many primes. The two main results are: 1) every such function is analytic in the upper half plane; 2) if such function takes the same value in two different points z 1 and z 2 then there exist an f
POLYNOMIAL ALGORITHM TO GENERATE INFINITELY MANY PRIME NATURAL NUMBERS
"... Abstract. For many years now, in the field of number theory, many mathematicians have failed at developing an algorithm that can generate infinitely many prime numbers. The idea of coming up with an algorithm that will generate infinite prime numbers has been a mystery for centuries. Mathematicians ..."
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Abstract. For many years now, in the field of number theory, many mathematicians have failed at developing an algorithm that can generate infinitely many prime numbers. The idea of coming up with an algorithm that will generate infinite prime numbers has been a mystery for centuries. Mathematicians
INTEGRAL DOMAINS HAVING NONZERO ELEMENTS WITH INFINITELY MANY PRIME DIVISORS
"... Abstract. In a factorial domain every nonzero element has only finitely many prime divisors. We study integral domains having nonzero elements with infinitely many prime divisors. Let D be an integral domain. It is well known that if D is a UFD then every nonzero element has only finitely many prim ..."
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Abstract. In a factorial domain every nonzero element has only finitely many prime divisors. We study integral domains having nonzero elements with infinitely many prime divisors. Let D be an integral domain. It is well known that if D is a UFD then every nonzero element has only finitely many
Automaticity of social behavior: Direct effects of trait construct and stereotype activation on action
 Journal of Personality and Social Psychology
, 1996
"... Previous research has shown that trait concepts and stereotypes become active automatically in the presence of relevant behavior or stereotypedgroup features. Through the use of the same priming procedures as in previous impression formation research, Experiment l showed that participants whose con ..."
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Cited by 542 (14 self)
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fulfilling prophecies are discussed, as is whether social behavior is necessarily mediated by conscious choice processes. For many years, social psychologists have studied the effects of priming on the individual's subsequent impressions of others. Priming refers to the incidental activation of knowledge
Some optimal inapproximability results
, 2002
"... We prove optimal, up to an arbitrary ffl? 0, inapproximability results for MaxEkSat for k * 3, maximizing the number of satisfied linear equations in an overdetermined system of linear equations modulo a prime p and Set Splitting. As a consequence of these results we get improved lower bounds for ..."
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Cited by 748 (11 self)
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We prove optimal, up to an arbitrary ffl? 0, inapproximability results for MaxEkSat for k * 3, maximizing the number of satisfied linear equations in an overdetermined system of linear equations modulo a prime p and Set Splitting. As a consequence of these results we get improved lower bounds
Variants of the Selberg sieve, and bounded intervals containing many primes
, 2014
"... For any m ≥ 1, let Hm denote the quantity lim infn→∞(pn+m − pn). A celebrated recent result of Zhang showed the finiteness of H1, with the explicit bound H1 ≤ 70, 000, 000. This was then improved by us (the Polymath8 project) to H1 ≤ 4680, and then by Maynard to H1 ≤ 600, who also established for ..."
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Cited by 10 (1 self)
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show the stronger statement that for any admissible triple (h1, h2, h3), there are infinitely many n for which at least two of n + h1, n + h2, n + h3 are prime, and also obtain a related disjunction asserting that either the twin prime conjecture holds or the even Goldbach conjecture is asymptotically
SPACINGS BETWEEN INTEGERS HAVING TYPICALLY MANY PRIME FACTORS
, 2009
"... We show that the sequence of integers which have nearly the typical number of distinct prime factors forms a Poisson process. More precisely, for δ arbitrarily small and positive, the nearest neighbor spacings between integers n with ω(n) − log 2 n  ≤ (log 2 n) δ obey the Poisson distribution l ..."
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We show that the sequence of integers which have nearly the typical number of distinct prime factors forms a Poisson process. More precisely, for δ arbitrarily small and positive, the nearest neighbor spacings between integers n with ω(n) − log 2 n  ≤ (log 2 n) δ obey the Poisson distribution
Results 1  10
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516,697