> ?Numbers are called Ruth-Aaron pair, such as {714, 715}. Are consecutive
> numbers {n, n +1} such that the sum of the prime factors of each are equal.
>
> Let's see
>
> 714 = 2x3x7x17
> 715 = 5x11x13
>
> Sum of divisors of 714 = 29 = Sum of divisors of 715
>
>
>
> FACTORS FOR EACH OF THE FOLLOWING TWO NUMBERS. COULD NOT DERIVE
>
> A number of 135 digits es1 Aoron
>
> *
> 296603151077074197308684124715622560525294501766069587161483751777320391554230009758029564174782423278870115094641644418265512090475910
> *
>
>
> The following of the former is
>
> *
> 296603151077074197308684124715622560525294501766069587161483751777320391554230009758029564174782423278870115094641644418265512090475911
> *
>
> The number is simply too big to be factored by Maxima's algorithm. ?You
> might like to try other software with better support for computational
> number theory, such as Pari/GP. ?I suspect that the numbers in question
> (from here <http://www.immortaltheory.com/NumberTheory/RuthAaron.htm>;) were
> produced by a polynomial, so all you need to do is to solve the appropriate
> polynomial f(x)=n, where n is the smaller of the two numbers.
>
As Alasdair points out, other software can do this better (and Maxima
does things e.g. Pari/GP doesn't do). Sage happens to include both
Maxima and Pari/GP, where you can either use them as wrapped by Sage
(to do things with both large numbers and integrals at the same time)
or you can use it as a convenient way to access both in the norma way.
Sage does tend to be a bit behind the most up-to-date version of
each.
These particular numbers are big enough, though, that any software
will take a little bit doing them.
----------------------------------------------------------------------
| Sage Version 4.7.1, Release Date: 2011-08-11 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: %time factor(296603151077074197308684124715622560525294501766069587161483751777320391554230009758029564174782423278870115094641644418265512090475910)
It still hasn't finished :)
If you are more specifically interested in certain types of
factorizations or primes, there may be even more optimized software,
e.g. the GIMPS uses a custom program to check Mersenne numbers for
primality.