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A complete Vinogradov 3primes theorem under the Riemann hypothesis
 ERA Am. Math. Soc
, 1997
"... Abstract. We outline a proof that if the Generalized Riemann Hypothesis holds, then every odd number above 5 is a sum of three prime numbers. The proof involves an asymptotic theorem covering all but a finite number of cases, an intermediate lemma, and an extensive computation. 1. ..."
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Abstract. We outline a proof that if the Generalized Riemann Hypothesis holds, then every odd number above 5 is a sum of three prime numbers. The proof involves an asymptotic theorem covering all but a finite number of cases, an intermediate lemma, and an extensive computation. 1.
New experimental results concerning the Goldbach conjecture
 Algorithmic Number Theory (Third International Symposium, ANTSIII
, 1998
"... and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of ..."
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and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of
Mathematical Developments in 1994 Paul J. Campbell
"... Introduction The most significant mathematical development in 1994 occurred near the end of the year, when Andrew Wiles (Princeton University) presented a revised proof of Fermat's last theorem, a year and a half after his first announcement of a proof and almost a year after he admitted that the f ..."
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Introduction The most significant mathematical development in 1994 occurred near the end of the year, when Andrew Wiles (Princeton University) presented a revised proof of Fermat's last theorem, a year and a half after his first announcement of a proof and almost a year after he admitted that the first proof contained a gap. Other mathematical developments and discoveries included further progress on another conjecture in number theory, the Goldbach conjecture; the revelation that the Intel Pentium computer chip makes numerical errors; the factoring of a 129digit integer that had been set as a challenge problem; the first example of "molecular computing" to solve a mathematical problem; and an argument over whether a spherepacking conjecture has been proved. In an unprecedented achievement, each of the six members of the U.S. team of highschool students participating in the International Mathematical Olympiad earned a perfect score in the competition. In June 1993, after seven ye
VERIFYING THE GOLDBACH CONJECTURE UP TO 4 · 10 14
"... Abstract. Using a carefully optimized segmented sieve and an efficient checking algorithm, the Goldbach conjecture has been verified and is now known to be true up to 4 · 10 14. The program was distributed to various workstations. It kept track of maximal values of the smaller prime p in the minimal ..."
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Abstract. Using a carefully optimized segmented sieve and an efficient checking algorithm, the Goldbach conjecture has been verified and is now known to be true up to 4 · 10 14. The program was distributed to various workstations. It kept track of maximal values of the smaller prime p in the minimal partition of the even numbers, where a minimal partition is a representation 2n = p + q with 2n − p ′ being composite for all p ′ <p. The maximal prime p needed in the considered interval was found to be 5569 and is needed for the partition 389965026819938 = 5569 + 389965026814369.