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每个不小于40的偶数都是两个奇素数之和

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发表于 2025-7-8 15:17 | 显示全部楼层 |阅读模式
每个不小于40的偶数都是两个奇素数之和
 楼主| 发表于 2025-7-8 15:19 | 显示全部楼层
本帖最后由 cuikun-186 于 2025-7-9 17:58 编辑

每个不小于 40 的偶数都是两个奇素数之和
作者:崔坤,独立研究员,中国青岛
摘要:
本文基于崔坤的哥德巴赫猜想表法数公式,结合素数分布理论,证明了每个不小于 40 的
偶数均可表示为两个奇素数之和。通过分析有序素数表法数 r2(N)的下界,并利用素数计数
函数(π(x)+1(假设 1 为素数))下界严格推导出 r2(N)≥1 对所有 N≥40 都成立,
从而证明了哥德巴赫猜想在[40,∞)内都正确性。
关键词:哥德巴赫猜想;容斥原理;共轭等差数列;奇素合数对个数;哥德巴赫猜想表法数
Abstract:
This paper establishes a proof of Goldbach's conjecture for all even numbers not
less than 18, based on Cui Kun's representation-counting formula combined with prime
distribution theory. By analyzing the lower bound of the ordered prime-pair counting
function r2(N) and employing an explicit lower bound of the prime-counting
function π(x)+1 (under the hypothesis that 1 is considered prime), we rigorously
derive r2(N)≥1 for all N≥40, thereby verifying the validity of Goldbach's
conjecture within the interval [40,∞).
Keywords:Goldbach's conjecture; inclusion-exclusion principle; conjugate
arithmetic progressions; count of odd prime-composite pairs; Goldbach
representation counting function. Every even number not less than 18 can be represented as the sum of two odd primes.
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 楼主| 发表于 2025-7-9 17:57 | 显示全部楼层
每个不小于 40 的偶数都是两个奇素数之和
作者:崔坤,独立研究员,中国青岛

摘要:
本文基于崔坤的哥德巴赫猜想表法数公式,结合素数分布理论,证明了每个不小于 40 的
偶数均可表示为两个奇素数之和。通过分析有序素数表法数 r2(N)的下界,并利用素数计数
函数(π(x)+1(假设 1 为素数))下界严格推导出 r2(N)≥1 对所有 N≥40 都成立,
从而证明了哥德巴赫猜想在[40,∞)内都正确性。
关键词:哥德巴赫猜想;容斥原理;共轭等差数列;奇素合数对个数;哥德巴赫猜想表法数
Abstract:
This paper establishes a proof of Goldbach's conjecture for all even numbers not
less than 18, based on Cui Kun's representation-counting formula combined with prime
distribution theory. By analyzing the lower bound of the ordered prime-pair counting
function r2(N) and employing an explicit lower bound of the prime-counting
function π(x)+1 (under the hypothesis that 1 is considered prime), we rigorously
derive r2(N)≥1 for all N≥40, thereby verifying the validity of Goldbach's
conjecture within the interval [40,∞).
Keywords:Goldbach's conjecture; inclusion-exclusion principle; conjugate
arithmetic progressions; count of odd prime-composite pairs; Goldbach
representation counting function. Every even number not less than 18 can be represented as the sum of two odd primes.

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