GPT-6-Astra项目形式化验证素数间隙上界

GPT-6-Astra项目使用Lean 4形式化验证和Python数值证明的结合，证明了存在无穷多对连续素数，其间隙距离至多为1861。这一证明基于Deligne定理和Kloosterman和等数学估计，通过条件性公理形式化了素数间隙界的证明1。

该项目采用了Lean 4.34.0-rc2、Python 3.12.13、NumPy 2.2.6和python-flint 0.9.0等工具1。数值证明依赖三个显式输入公理——Kloosterman3_bound、Kloosterman2_correlation_bound和physical_integral_bounds1，其中包含104个外层和45个内层物理积分上界，加3个上限界1。形式化验证通过执行命令python3 -B prime_gap_186_certificate.py --workers 4 --output prime_gap_186_fresh.json完成1，验证过程通过Lean内核和Comparator检查，无错误或警告1。

The GPT-6-Astra project has successfully demonstrated that infinitely many pairs of consecutive primes exist with a maximum gap of 186 using both formal verification and numerical proof methods 1. The research combines Lean 4 formal verification with Python numerical computation, building upon mathematical foundations including Deligne's theorem and Kloosterman sum estimates to establish this bound on prime gaps 1.

The verification framework relies on three explicit input axioms—Kloosterman3_bound, Kloosterman2_correlation_bound, and physical_integral_bounds—which underpin the conditional formalization of the prime gap inequality 1. The numerical proof component comprises 104 outer-layer and 45 inner-layer physical integral bounds alongside three additional limit bounds 1. The project employs Lean 4.34.0-rc2 alongside Python 3.12.13, NumPy 2.2.6, and python-flint 0.9.0 to execute the proof, with numerical verification initiated through the command python3 -B prime_gap_186_certificate.py --workers 4 --output prime_gap_186_fresh.json 1. The formalized proof passes validation by both the Lean kernel and Comparator verification tools without errors or warnings 1.