Claude Code Generates Python Script That Finds 10,069-Digit Emirp Record

Claude Code, using Anthropic's Opus 4.6 model, generated a Python script that found a 10,069-digit emirp (reversible prime number) in approximately one day of CPU time, setting a new world record. The user provided Claude with a Numberphile video about the previous record and asked it to beat that record on a personal computer.

Technical Implementation

Claude initially created a Python script that could find the emirp within "a few days of runtime." Through further discussion, it produced an optimized version with four successive tiers of prime sieves. The optimization included:

• A "ludicrously fast CUDA kernel for generating random numbers with no factor smaller than 2³²"
• Pure brute force approach without algebraic shortcuts
• No "unsatisfying strings of zeroes" in the output

The user notes they are "neither a mathematician nor a full time programmer" and that "most of the algorithms implemented I had never heard of until yesterday."

Output and Verification

The resulting number is a 'BPSW probable' emirp, which provides strong probabilistic verification of primality but isn't yet rigorous proof. The user is working on formal proof using primo software. The 10,069-digit number was generated through this process.

The approach contrasts with the previous record attempt described in the Numberphile video, which used "arithmetic hacks and drew on extensive effort and knowledge from prime finding communities."