[quote=10metreh;196183]That (2^3 * 3) is a driver, but it's the easiest to escape of all drivers, especially while the 3 is squared.[/quote]

ok I thought that 2^3 * 3 was a guide... :smile:

---

Done with 723120
index 1247, 104 digits, 2^2 * 3 * 7

Done with [code]728640 [B]3554.[/B] 2^4 * 3 * 5 * 31 c94 sz 101[/code]
This one went down from 92 to 11 digits (took several downdriver runs), but then it acquired 2^3 * 3 at 31 digits, that soon changed directly into 2 * 3, and that changed directly into 2^3 * 3 * 5, which changed directly into 2^4 * 31 at 95 digits. Life is sad sometimes. :sad:

[quote=10metreh;196183]That (2^3 * 3) is a driver, but it's the easiest to escape of all drivers, especially while the 3 is squared.[/quote]
I don't think it is a driver unless it has a factor of 5 and the exponent of 3 is one - so specifically 2^3*3^1*5

Anything else isn't fully supported - the powers of two from the 'one more than the odd terms' must be greater or equal to the power of two.

So for example 2^3*3 has only two twos from 3+1 which is less than the 3 of 2^3 so it is not a driver.

Another way of stating it is that it cannot change the power of 2 unless one of the odd terms is a power higher than 1. So [driver]*p where p = 1 mod 4 doesn't escape.

[quote=Greebley;196219]I don't think it is a driver unless it has a factor of 5 and the exponent of 3 is one - so specifically 2^3*3^1*5
...[/quote]
[url]http://www.mersennewiki.org/index.php/Aliquot_Sequences[/url]
2^3 * 3 is a driver (an easy-to-break and slow-growing one), as well as 2^3 * 3 * 5 (a tough-to-break and fast-growing one).

done with 720912
reserving 723432

Done with 725052 729792 727596 and 729660

Ok, you are right. I looked at the Analysis and Class 1 (ones that can escape without a square term on the odd number if they get [driver]*p where p is 1 mod 4) is called a driver so that 2 can be included in the drivers. This has the side effect of including 2^3*3 as a driver as well.

I personally don't consider 2^3*3^2*5 to be a driver because this is class 2 and the exponent of 3 can't be lowered to 1 unless 5 is square. 2^5*3^2*7 can never go to 3^1 without changing the power of 2 so this one remains class 2. The analysis doesn't specifically mention these cases though so I am not sure if they are officially not drivers.

-----------
Done with 721364, 114 digits, 2^3*3*5*7

[QUOTE=Greebley;196275]Ok, you are right. I looked at the Analysis and Class 1 (ones that can escape without a square term on the odd number if they get [driver]*p where p is 1 mod 4) is called a driver so that 2 can be included in the drivers. This has the side effect of including 2^3*3 as a driver as well.[/QUOTE]

Actually the definition of a driver is that, for [tex]2^an[/tex], [tex]n\mid\sigma(2^a)[/tex] and [tex]2^{a-1}\mid\sigma(n)[/tex].

done with 723432
reserving 723480

[quote=10metreh;196282]Actually the definition of a driver is that, for [tex]2^an[/tex], [tex]n\mid\sigma(2^a)[/tex] and [tex]2^{a-1}\mid\sigma(n)[/tex].[/quote]

Actually that is the same thing, just stated more technically. The -1 in a-1 of the second expression is why class 1 is counted. In fact:
[tex]2^{a-<class>}\mid\sigma(n)[/tex]

Reserving 726354