[新聞] 兩個質數猜想
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這兩天解析數論界相當忙碌,
因為兩個重要的質數猜想有重大進展;
首先是 odd Goldbach conjecture,
Conj. 每個大於 5 的奇數都可以寫成三個質數的和.
Helfgott 昨天在 Arxiv 上公布了
http://arxiv.org/abs/1305.2897 Major arcs for Goldbach's theorem
與他之前一篇論文
http://arxiv.org/abs/1205.5252 Minor arcs for Goldbach's problem
合起來算是解決了這個猜想.
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另外有傳言 University of New Hampshire 的 Yitang Zhang (找不到資料?)
證明了一個弱的孿生質數猜想,
Conj. 有無限組質數對 (p,q) 滿足 |p - q| < N.
http://www.math.columbia.edu/~woit/wordpress/?p=5865
http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989
宣稱的 N 大約是 70000000 (七千萬).
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