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.