Fermat.nb

The converse of Fermat's Little Theorem is False - another example

Which of the odd numbers from 547 to 567 are prime?

`m`	$"\!\(5\^m\)"$	`≡(mod m)`
`547`	${"5"}^{546}$	`1`
`549`	${"5"}^{548}$	`286`
`551`	${"5"}^{550}$	`480`
`553`	${"5"}^{552}$	`141`
`555`	${"5"}^{554}$	`250`
`557`	${"5"}^{556}$	`1`
`559`	${"5"}^{558}$	`428`
`561`	${"5"}^{560}$	`1`
`563`	${"5"}^{562}$	`1`
`565`	${"5"}^{564}$	`60`
`567`	${"5"}^{566}$	`340`

Select [Range [547, 567], PrimeQ]

{547, 557, 563}

Converted by Mathematica April 24, 2000