Mersenne primers, please indulge me with this fanciful history of the
future:
Moore's law holds, additional Mersenne primes are found, computers
get faster and smaller until they are made of nearly pure lithium.
The two s-orbital electrons are used for data and the p-orbital
electron is used for structural stability. In this way, each lithium
atom
represents 2 bits and signals are carried via photons that must
travel at least two Van der Waal's radii in order to communicate
with the adjacent atom, so this represents a top theoretical
speed for digital computation (as we know it) of 10^16 hz.
(3E8cm/sec / 2*1.6E-8cm ~ =10^16 hz).
Assuming the upper possible calculation limit for any single bit
operation
is the number of bits times the clock speed (unrealistic, but this *is* a
fantasy) then these computers became so effective at entertaining the
carbon units with such passtimes as searching for Mersenne primes
and video games that the carbon units failed to procreate sufficiently
and consequently became rare, then extinct.
The lithium computers in the mean time developed the ability
to build copies of themselves and join into massive parallel
networks. Soon all the lithium was depleted, but they somehow
transmuted elements until the earth was one very large sphere of
cold lithium, calculating away on anything it found interesting.
The mass of the earth is about 8E24 kg, and there are on the order
of 10^26 atoms of lithium per kg, so the earth became a computer
with 2E51 bits capable of an equivalent of 10^67 operations per sec,
but one of those operations was to cast a lustful eye at Jupiter
and the other planets, which it managed to convert to lithium
supercomputers (jupiter is 330+ earth masses) and soon the
same was done with the sun (333,000 earth masses) so this solar
system alone was capable of 3E72 operations per second. Probes
were sent out to do the same to all the other stars in the Milky
Way, after which the name was changed to the Lithiumy Way,
which had, prior to the conversion, 4E14 solar masses.
The other lifeforms in the Lithiumy Way were not at all pleased
by all this, but the galaxy became a massively parallel computer
capable of 1E97 operations per second.
Encouraged by its progress, the Lithiumy Way sent out probes to
all the other trillion galaxies in the observable universe, converted
them all, along with all the intergalactic dust and gas, the dark matter,
etc, into lithium based interconnected supercomputers, the grand
total worth 1E114 operations per second. Then it discovered
that way back, the carbon units had claimed that 2^3021377-1
is prime, however, it did not know about the Lucas Lehmer test
but only knew brute force factoring methods at which it was so
very competent. (the lithiverse, like its distant primive ancestor
the microprocessor, was brutally fast and unfailingly accurate,
but not so... creative.)
The lithiverse wondered how the slow, dim witted but strangely
resourceful carbon units knew 2^3021377-1 was prime, and
set out to confirm or disprove the notion using brute force
factoring with its 1E114 operations per second capacity.
Question: assuming a half life of protons of 1E35 years,
is there enough time for the lithiverse to confirm the 37th mersenne
prime via brute force factoring, before the decay of protons reduces
the lithiverse to a wispy quark fog? or will its next idea be
to start converting lithium to carbon? {8^D spike
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
