Miller's Primality Test

If a number fails this test, it is not a Prime. If the number passes, it may be a Prime. A numberpassing Miller's test is called a Strong Pseudoprime to base . If a number does not pass the test, then itis called a Witness for the Compositeness of . If is an Odd, PositiveComposite Number, then passes Miller's test for at most bases with (Long 1995).There is no analog of Carmichael Numbers for Strong Pseudoprimes.

The only Composite Number less than which does not have 2, 3, 5, or 7 as a Witness is3215031751. Miller showed that any composite has a Witness less than if the Riemann Hypothesisis true.

References

Long, C. T. Th. 4.21 in Elementary Introduction to Number Theory, 3rd ed. Prospect Heights, IL: Waveland Press, 1995.

• de la Loubere's Method
• Delannoy Number
• Delaunay Triangulation
• Delian Constant
• Delian Problem
• de Longchamps Point
• Del Pezzo Surface
• Delta Amplitude
• Delta Curve
• Delta Function
• Deltahedron
• Delta Sequence
• Delta Variation
• Deltoid
• Deltoidal Hexecontahedron
• Deltoidal Icositetrahedron
• Deltoid Caustic
• Deltoid Evolute
• Deltoid Involute
• Deltoid Pedal Curve
• Deltoid Radial Curve
• de Mere's Problem
• Demlo Number
• de Moivre-Laplace Theorem
• de Moivre Number