34 citations · 84 across the 17 of their papers we have counts for
7 papers · 1 filter
An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test
Jon Grantham
In a 2006 paper, Damgård and Frandsen designed a faster version of the Quadratic Frobenius Test. This test assumes the Extended Riemann Hypothesis in order to find small nonresidue…
There are Infinitely Many Perrin Pseudoprimes
Jon Grantham
This paper proves the existence of infinitely many Perrin pseudoprimes, as conjectured by Adams and Shanks in 1982. The theorem proven covers a general class of pseudoprimes based…
A Probable Prime Test With High Confidence
Jon Grantham
Monier and Rabin proved that an odd composite can pass the Strong Probable Prime Test for at most of the possible bases. In this paper, a probable prime test is develope…
Frobenius Pseudoprimes
Jon Grantham
The proliferation of probable prime tests in recent years has produced a plethora of definitions with the word ``pseudoprime'' in them. Examples include pseudoprimes, Euler pseudop…
The Largest Prime Dividing the Maximal Order of an Element of
Jon Grantham
We define to be the maximal order of an element of the symmetric group on elements. Results about the prime factorization of allow a reduction of the upper bound…
Repeatedly Appending Any Digit to Generate Composite Numbers
Jon Grantham, Witold Jarnicki, John Rickert +1
We investigate the problem of finding integers such that appending any number of copies of the base-ten digit to yields a composite number. In particular, we prove that…