Given the Lucas sequence and , define . Then an extra strong Lucas pseudoprime to the base is a composite number , where is odd and such that either and , or for some with . An extra strong Lucas pseudoprime is a strong Lucas pseudoprime with parameters . Composite are extra strong pseudoprimes for at most 1/8 of possible bases (Grantham 1997).
Extra Strong Lucas Pseudoprime
See also
Lucas Pseudoprime, Strong Lucas PseudoprimeExplore with Wolfram|Alpha
References
Grantham, J. "Frobenius Pseudoprimes." http://www.pseudoprime.com/pseudo1.psGrantham, J. "A Frobenius Probable Prime Test with High Confidence." 1997. http://www.pseudoprime.com/pseudo2.psJones, J. P. and Mo, Z. "A New Primality Test Using Lucas Sequences." Preprint.Nicely, T. R. "The Baillie-PSW Primality Test." http://www.trnicely.net/misc/bpsw.html.Referenced on Wolfram|Alpha
Extra Strong Lucas PseudoprimeCite this as:
Weisstein, Eric W. "Extra Strong Lucas Pseudoprime." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ExtraStrongLucasPseudoprime.html