the basis for methods with much smaller error bounds. Note that these have more steps, additional requirements, and non-negligible additional computation beyond what is described on this page. It is important to note that the error bounds for these methods do not apply to the standard or strong Frobenius tests with fixed values of (P,Q) described on this page. Based on this idea of pseudoprimes, algorithms with strong worst-case error bounds can be built. The quadratic Frobenius test, using a quadratic Frobenius test plus other conditions, has a bound of . Müller in 2001 proposed the MQFT test with bounds of essentially . Damgård and Frandsen in 2003 proposed the EQFT with a bound of essentially . Seysen in 2005 proposed the SQFT test with a bound of and a SQFT3 test with a bound of . Given the same computational effort, these offer better worst-case bounds than the commonly used Miller–Rabin primality test. See also Pseudoprime Lucas pseudoprime Ferdinand Georg Frobenius Quadratic Frobenius test References External links Jacobsen, Dana Pseudoprime Statistics, Tables, and Data (data for Frobenius (1,-1) and (3,-5) pseudoprimes) Pseudoprimes