Largest known probable prime cofactors of Phi(x, n!)  (proper divisor of Phi(x, n!) with x = 1 to 24)

x = 1 and 2:
Phi(1, n!) = n!-1:   3 largest known > 10000 digits
Phi(2, n!) = n!+1:  6 largest known > 10000 digits

x = 3 to 24:

Cofactor	Digits	When
Phi(7, 2210!)/(2591 . 46061 . 571659817)	38584	03/2006
Phi(12, 2988!)/2105069497	36347	03/2006
Phi(6, 4561!)/952117	29415	02/2006
Phi(18, 1629!)/(94320901 . 3123429823)	27144	02/2006
Phi(6, 4112!)/3522667	26149	02/2006

MultiSieve (written by Mark Rodenkirch) was used to find the factors < 2³⁴

All probable prime cofactors on this page have passed a Miller-Rabin primality test in 10 randomly chosen bases (ispseudoprime test in PARI/GP). All probable prime cofactors on this page were found by me and are listed on Henri Lifchitz's Top 10000 PRPs page. Click here to view the 25 largest known probable prime cofactors of Phi(x, n!) for x = 3 to 24.

Bernardo Boncompagni's n!±1 Factorizations
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Last updated on October 26, 2006
Donovan Johnson