But (assuming n is composite) no prime factor of n can be greater than
n^0.5. So how can n^0.6065 be the average?
(I hope I'm not showing my idiocy here! :)
Kyle Evans (newbie on this list)
-----Original Message-----
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED]]On Behalf Of Jud
McCranie
Sent: Sunday, January 23, 2000 4:00 PM
To: Pierre Abbat
Cc: [EMAIL PROTECTED]
Subject: Re: Mersenne: Size of largest prime factor
At 03:48 PM 1/23/00 -0500, Pierre Abbat wrote:
>If I pick a huge number n at random, how much smaller than n, on average,
is
>its largest prime factor?
On the average, the largest prime factor of n is n^0.6065, and the second
largest is n^0.2117. Reference: Knuth, the Art of Computer Programming,
vol 2, section 4.5.4.
+--------------------------------------------------------+
| Jud McCranie |
| |
| 137*2^197783+1 is prime! (59,541 digits, 11/11/99) |
| 137*2^224879+1 is prime! (67,687 digits, 1/00) |
+--------------------------------------------------------+
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