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math/big: ProbablyPrime skips Miller–Rabin rounds when n is MaxInt #81491
Description
(*Int).ProbablyPrime(math.MaxInt) overflows the Miller–Rabin round count and skips that test entirely. As a result, it reports the composite integer 10877 as probably prime, contrary to the documented accuracy for inputs below 2^64.
x := big.NewInt(10877) // 73 * 149
fmt.Println(x.ProbablyPrime(0), x.ProbablyPrime(1), x.ProbablyPrime(math.MaxInt)) // false false trueDetails
In src/math/big/prime.go, ProbablyPrime passes n+1 to probablyPrimeMillerRabin. For n == math.MaxInt, this becomes a negative int; the helper’s for i := 0; i < reps; i++ loop executes no rounds and returns true. Only the Lucas test remains after the earlier filters.
This issue was found by zkao and was triaged by @FiloSottile as a valid bug but not a vulnerability. /cc @golang/security
Activity
gabyhelp commentedon Sep 13, 2026
Related Issues
(Emoji vote if this was helpful or unhelpful; more detailed feedback welcome in this discussion.)
math/big: cover ProbablyPrime round-count boundaries
gopherbot commentedon Sep 17, 2026
Change https://go.dev/cl/834124 mentions this issue:
math/big: avoid overflow in ProbablyPrime round countcherrymui commentedon Sep 18, 2026
cc @griesemer @thatnealpatel @golang/security
math/big: cover ProbablyPrime round-count boundaries