From Jun 5-11, 2026 contributions came from Rahid Zaman, Gennady Gusev, J. M. Rebert, Paul Cleary

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N.B. by CR: 1002887 is first "missing prime" in the first one hundred million digits of π. [De Geest]", on March 2002. .

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Rahid wrote:

Using a streaming digit scan, I verified the known result for the first 10^6 digits of pi:

n = 6: 100057

I then found the following results for larger powers:

n = 7: 211889

n = 8: 1002887

n = 9: 10036087

Here I counted digits after the decimal point. For n = 9, I verified the result with two independent digit sources: streamed PILookup chunks and MIT’s one-billion-digit pi file.

The method was to scan the digit stream once, mark every observed k-digit block in compact bitsets, then iterate primes with primesieve and return the first prime whose decimal representation was not observed.

A note on credit: this was primarily AI-assisted computational work. I gave the puzzle to OpenAI Codex, used GPT-5.5 Pro to help research and optimize the approach, and then used Codex to implement and run the verification. My role was mainly prompting, supervising, relaying the optimization plan, and checking that the result was verified against independent digit sources.

If useful, I’m happy to send the source files and run notes. Please feel free to list the result as AI-assisted, or however you think is appropriate


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Gennady wrote:

The first missing primes for the first 10^n digits of pi are:

n=7 p=211889

n=8 p=1002887

n=9 p=10036087

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Jean Marc wrote:

For n = 7, 8 and 9, I found respectively 211889, 1002887 and 14706667.

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Paul wrote

FIRST MISSING EMBEDDED PRIME FOUND
Pi digits tested = 100000000
first missing prime = 1002887
prime digit length = 7
elapsed = 0h 1m 32s


FIRST MISSING EMBEDDED PRIME FOUND
Pi digits tested = 1000000000
first missing prime = 10036087
prime digit length = 8
elapsed = 0h 56m 18s