Wall-Sun-Sun Prime Checker
Check Fibonacci-Wieferich/Wall–Sun–Sun congruence F_(p−(5/p)) mod p² for actual primes other than 2 and 5 using exact modular doubling; excluded/nonprime inputs explicitly not applicable, no existence claim.
Description
A Wall–Sun–Sun test concerns a Fibonacci congruence modulo a prime squared.
A Wall–Sun–Sun test concerns a Fibonacci congruence modulo a prime squared. Primes 2 and 5 require exclusion from this particular Legendre-symbol formulation.1
Check Fibonacci-Wieferich/Wall–Sun–Sun congruence F_(p−(5/p)) mod p² for actual primes other than 2 and 5 using exact modular doubling; excluded/nonprime inputs explicitly not applicable, no existence claim.
When to use Wall-Sun-Sun Prime Checker
Use this tool to check Fibonacci-Wieferich/Wall–Sun–Sun congruence F_(p−(5/p)) mod p² for actual primes other than 2 and 5 using exact modular doubling; excluded/nonprime inputs explicitly not applicable, no existence claim.
Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
How to use Wall-Sun-Sun Prime Checker and understand its results
- Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
- Enter candidatePrime using the field table and calculation rules, then run the tool.
- Read isPrimeCandidate, testApplicable, fibonacciModuloPrimeSquared, isWallSunSunPrime. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| candidatePrime | Candidate prime | number | Required |
Enter an integer candidate from 2 to one million. Test primality; composites and 2 or 5 return testApplicable false, residue string "0" and result false. For other primes derive the symbol from p mod 5 and use exact BigInt Fibonacci doubling modulo p².
test F[p−(5/p)] mod p² = 0 Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| isPrimeCandidate | Is prime candidate | boolean |
| testApplicable | Test applicable | boolean |
| fibonacciModuloPrimeSquared | Fibonacci modulo prime squared | string |
| isWallSunSunPrime | Is wall sun sun prime | boolean |
{
"input": {
"candidatePrime": 5
},
"output": {
"isPrimeCandidate": true,
"testApplicable": false,
"fibonacciModuloPrimeSquared": "0",
"isWallSunSunPrime": false
}
}Limitations and assumptions
The zero residue on inapplicable inputs is a placeholder, not a successful congruence. A bounded test makes no existence or completeness claim.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.
Alternative or Complementary methods
Use Pillai Prime Checker: Find exact Pillai prime witnesses k!≡−1 mod p with k not dividing p−1; exhaustive bounded k<p, no inferred classification from one arbitrary k. For a complementary task, use Prime Triplet Checker: Check supplied prime-triplet patterns (p,p+2,p+6) or (p,p+4,p+6), plus exceptional (3,5,7); not any three primes or a twin-pair alias.
References
-
Wall-Sun-Sun Prime Checker — tool.io
Similar or alternative tools
- Pillai Prime Checker
Find exact Pillai prime witnesses k!≡−1 mod p with k not dividing p−1; exhaustive bounded k<p, no inferred classification from one arbitrary k.
- Prime Triplet Checker
Check supplied prime-triplet patterns (p,p+2,p+6) or (p,p+4,p+6), plus exceptional (3,5,7); not any three primes or a twin-pair alias.