Limits RegistryPUBLIC RECORD
Limits RegistryThe largest known Sophie Germain prime is 2618163402417 x 2^1290000 - 1, with 388,342 digits, found by PrimeGrid in February 2016; 2p+1 is then also prime (a 'safe prime'). Sophie Germain primes are named after the French mathematician who used them in her work on Fermat's Last Theorem.
The question, scope, and sources behind this Registry record.
The largest known Sophie Germain prime is 2618163402417 x 2^1290000 - 1, with 388,342 digits, found by PrimeGrid in February 2016; 2p+1 is then also prime (a 'safe prime'). Sophie Germain primes are named after the French mathematician who used them in her work on Fermat's Last Theorem.
The largest known prime p such that 2p+1 is also prime.
Change a parameter to stress-test whether a proposed result is still inside the published specification. This is an audit aid, not a proof checker.
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Current frontiers derived from accepted Claims.
An observed or demonstrated result; no opposing bound is implied.
The frontier is not sacred
Most progress starts with a disagreement that survives contact with evidence. If you can push the known lower bound up or pull the upper bound down, show us the work.
≥ when you have shown that at least this value is achievable.≤ when you have shown that anything above this value is impossible.No vibes. State the value, define the scope, and link the paper, proof, code, or reproduction that lets another person check it. Editors review every challenge before the public record changes.
Challenge this recordAssertions tied to evidence, attribution, and review.
The frontier as it changed over time.
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.
1 accepted Claim, with 1 linked evidence records.
Permanent ID limitsregistry.com/limits/LR-LARGEST-KNOWN-SOPHIE-GERMAIN-PRIME
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Limits Registry. LR-LARGEST-KNOWN-SOPHIE-GERMAIN-PRIME. Largest known Sophie Germain prime. 2026.