每个不小于40的偶数都是两个奇素数之和

cuikun-186

每个不小于40的偶数都是两个奇素数之和

cuikun-186

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.

cuikun-186

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.