素数2^127 - 1的150周年纪念
The sesquicentennial of the prime number $2^{127} - 1$
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中文总结 AI 辅助
本文纪念2^127 - 1素数发现150周年，回顾其历史，给出卢卡斯-莱默检验法的现代证明，该方法是验证大素数的核心工具。
中文摘要 AI 辅助
2026年标志着一项数学领域非凡成就的150周年纪念：1876年，法国数学家爱德华·卢卡斯证明了39位数M₁₂₇:=2^127 - 1是素数。该素数作为已知最大素数的地位维持了75年，至今仍是无需借助机械装置发现并验证的最大素数。本文回顾这一发现背后的历史，并给出密切相关的卢卡斯-莱默检验法的现代证明，该方法至今仍是验证大素数的核心工具。
英文摘要
The year 2026 marks the 150th anniversary of a remarkable achievement in mathematics: in 1876, the French mathematician Édouard Lucas showed that the 39-digit number $M_{127} := 2^{127} -1$ is prime. This stood for 75 years as the largest known prime, and it remains the largest prime number discovered and certified without the aid of a mechanical device. We review the history behind this discovery and give a modern proof of the closely related Lucas-Lehmer test, which is still the main engine behind the certification of large prime numbers.
