SIX
6 is the first perfect number.
6=3+2+1 the sum of all
its factors except itself.
is
the thirteenth perfect number discovered in 1952.
(2521-1)
world record
Mersenne prime for about one hour.
Euclid's form, 
is
perfect if 
is prime.
is
the 43nd Mersenne prime, Dec. 15, 2005, GIMPS
Here it is.
Over 9 million digits long. Likely a $100,000.00 prize for the next, if
over 10 million digits.
is
the 42nd Mersenne prime, Feb 26, 2005, GIMPS
The corresponding
perfect numbers are huge.
(GIMPS:
Great Internet Mersenne Prime Search, not exactly politically correct
terminology)
Whether
they are finite of infinite is still unanswered (very sparce).
6 is the second hexagonal number, n(2n-1)
Eight
8 is the first cube 2x2x2.
All numbers can be expressed as the sum of no more than 9 cubes.
g(3) =
9 and G(3) is less than or equal to 8.
G(3) is the number of
cubes required to express any number excluding a finite number of them.
Hardy-Ramanujan's 1729 sum of 2 cubes 2 ways.
Called a taxicab number.
1729 is the third Carmichael number.
Nine
Computation checking technique known as "casting out 9s".
For example: suppose you want to multiply
12,934 x
42,456=549,125,904
1+2+9+3+4=19,
1+9=10,
1+0=1
id est 12,934 = 1 mod 9
4+2+4+5+6=21, 2+1=3
id est 42,456 = 3 mod 9
5+4+9+1+2+5+9+0+4=39, 3+9=12, 1+2=3.
id est 549,125,904 = 3 mod
9
1 x 3 = 3 (Check complete)
Based on 10x/9 always having a remainder
of 1.
This technique was used with calculations using the abacus also was a
popular vlsi technique called concurrent checking.
The difference was the base and the number of papers produced :)
Quiz 2: What modulus is used for
concurrent checking in digital logic vlsi
papers?
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