[extropy-chat] Goldbach's Conjecture Resolved! A Story

[Lee Corbin]

The singularity happened all right. Everyone got uploaded, even the
dead people, and lived happily ever after.

Only that *wasn't* the end of the story.

The vast superhuman intelligences whose influence had radiated out
from the Milky Way had other things on their minds besides keeping
tiny patterns of ancient life alive and happy. There was still the vexing
problem of unifying forces and particles. And somehow, despite
millions of years, mysteries yet remained about black holes.

Finally, however, there was progress, and an ultimate explanation
uncovered.  As had been guessed by even the primitive parental life
forms at the dawn of time, our entire infinite cosmos itself
is just the grown-up version of a little baby universe.

Moreover, our universe was no accident, but the contrivance of a yet
larger mother universe. Specifically, entities perhaps not unlike the
intelligences of our universe had deliberately spawned Bruno. (Our
universe had always been called "Bruno" in the honor of the spot of
dawn-life protoplasm which had first suspected its infinitude).

The values of the physical constants were unambiguous, and there was,
after all, a reason for our universe to exist.  A very specific reason:  our
mission was to settle Goldbach's conjecture.

This numerical conjecture was formulated in our universe in 1742 by one
Christian Goldbach, an amateur mathematician who occasionally
corresponded with Euler. The peculiarity he'd noticed is that every even
number beyond 2 seems to be the sum of two primes.  4 = 2 + 2,
6 = 3 + 3, 8 = 3 + 5, and so on. (The interested reader should find the
primes that add up to 98.)

Despite some mathematicians, like Lev Landau who snorted
"prime numbers are meant to be multiplied, not added!", the problem
remained tantalizing. Somehow, often just barely, the proof, if there
was one, evaded all attempts to find it ever since the first day Goldbach
and Euler had sought it.

Not even the local-cluster superintelligences  circa ten million A.D. had
been able to crack it.

Still, it was terribly shocking---if it can be said that such august intelligences
can undergo anything like shock---to find that the physical constants from a
whole range of interweaving theories actually coded up a request from the
laboratory of the sentients who created our universe!

The request was simple. Determine whether the particular number 

    428 08791  39342 94963  22581 56917  17541 83578  75376 65202
30935 79270  91986 99286  45236 44720  81915 70881  45886 43213
49789 97081  16075 20517  69980 25310  91953 01759  67635 88933
54558 18395  73375 62251  58871 09870  70538 48936  07757 90374
70335 18884  54411 23218  12023 05189  70669 55571  78420 44007
97817 88202  06270 36316  53840 91881  16009 21247  22901 38941
58239 27805  49141 57583  96679 43990  11760 58746  35093 08313
72354 56592  67977 51532  61668 96711  41036 71134  71509 10799
51406 57480  08102 60459  24867 28134  75408 07101  68550 79511
59551 94957  92832 00848  71220 64809  08250 76660  36595 80118
50816 25608  19626 95631  55333 85186  93223 20588  05216 04250
61353 76722  80519 48499  26442 15542  34664 37800  65787 71306
65777 22276  33654 29778  40999 46652  97751 17836  51838 37896
04227 00830  16324 19256  33927 15039  50507 69866  98133 86990
61439 63020  57279 11017  62260 12829  34206 75441  39698 81813
72912 44241  61421 17920  22848 68700  71139 87233  02937 69048
35630 08745  94170 61178  16545 95515  60049 13814  80083 97215
27350 06826  70114 17405  69154 64851  57318 16358  46942 59186
34226 06427  73694 77673  33441 20156  34436 31512  24280 73615
59712 38780  62647 40933  49338 91831  49401 29600  33633 94829
11705 37774  43834 86045  54417 56377  23385 77367  55138 85611
82640 36179  42736 61012  34102 12296  56058 91195  75411 07815
16789 86115  49187 12812  55606 44925  73938 74517  78859 73627
15945 35118  79582 03377  29331 61615  09411 26993  53856 86440
60411 82745  33726 31970  84558 02325  18014 26638  75442 09328
27453 34357  01020 13765  77838 05223  90178 99824  36756 18708
38180 65976  45518 23708  00000 56319  38851 68670  74234 55867
06495 01958  87811 29618  61051 77381  96741 38997  38430 84260
12366 99757  06711 97604  36860 72720  38282 23614  76723 10217
76292 07219  97214 69233  44691 01597  13884 31217  90811 08935
16527 92701  25590 65111  05580 56461  08618 10462  07467 32005
40944 46299  34679 25340  94871 30861  84123 95728  76596 27683
08719 92930  19326 76049  82379 98582  77499 68297  56203 26289
42185 22528  84434 83676  36579 48079  08317 23567  90955 92648
19977 84374  56968 81569  95674 23876  52827 33131  52802 82397
77050 18678  58735 55448  13527 23499  28271 64870  19095 05899
35087 45698  16275 72819  79894 23004  15926 53589  79323 84600
56631 88862  30487 38794  36079 32712  11130 55451  25137 38785
83558 31960  69473 45950  18225 09871  88502 75179  11551 75664
74321 67351  27703 83717  18913 42470  08816 37627  14288 62831
44047 67612  72738 26995  50933 63758  50003 43693  52661 55852
52372 59042  37595 04931  73622 68387  86478 40997  05245 75300
24902 59609  35653 15970  37681 69365  22236 86374  65550 00343
98377 35354  65770 15365  41422 71356  16630 40044  19290 66449
53629 79452  71674 30260  97303 06487  62789 13005  70152 22501
49867 89294  59232 31776  54919 99851  05438 01096  72269 50486
16719 06144  82041 38332  64452 31840  99287 59928  25503 08407
46970 45907  99238 74547  19704 72035  26542 54600  79172 58779
35747 78956  11478 41195  58135 63856  33037 45753  60159 25193
71838 07526  07985 60714  88627 75790  38454 96110  39237 19792
34534 70169  24805 63215  38175 38784  38855 24826  50917 25147
17082 26997  32295 10894  21805 65245  85407 37926  69214 38579
84721 23544  88548 65626  75517 69737  55626 52175  21697 19453
16908 82841  24060 40285  19195 80281  89322 15232  70043 60691
86370 91949  19017 83846  77869 14321  95102 87073  71467 31305
64677 80358  52629 79419  22359 87867  48296 50141  46807 82184
95812 84665  74511 59914  04146 90417  58508 62875  17630 21868
09199 30322  33352 43374  25473 04119  63086 14147  14863 38020
44757 98628  57916 22199  11865 42911  62651 78290  09392 77294
63168 21043  17409 13786  27475 75979  89668 43596  74316 84489
54941 95992  45445 41059  55142 15214  42903 16799  88254 95984
48575 77822  21067 57238  35352 96779  89564 23797  99937 46379
27119 16060  30302 95327  12849 38111  97090 07598  78473 63079
18570 72803  70040 91385  96436 96263  17368 56188  85999 50026
36050 73736  13351 48321  28357 51718  65636 72903  21584 21060
39829 15564  04716 14594  22363 97639  65937 17802  31535 42767
98761 30987  57657 33398  63053 25926  20944 19306  81727 02695
97479 79172  72764 66446  78864 12698  15812 97209  38827 91016
91281 57875  45228 49211  69755 99224  43999 62879  08879 80015
74396 57146  64665 31159  06980 79069  37409 75037  69977 85919
42826 06974  61063 97640  13433 92528  91311 08440  38840 22362
93929 01836  36590 75052  89475 15437  65648 99012  70236 12307
83585 00414  62851 48787  28447 21702  57033 29633  44760 34165
27548 37516  24343 63046  02081 20378  19510 42226  97134 68739
32982 56455  53129 77693  25022 55534  99375 30086  98001 07432
67126 76656  29347 28492  43108 64736  32278 84816  80440 30461
00818 09136  01952 48442  91058 92590  10443 05195  34009 32141
62209 43740  54102 76895  98172 31583  04155 66492  58981 16591
11331 06838  03818 77063  12523 45570  68970 70055  77751 73743
71732 04704  61384 57343  66682 44500  89745 10436  67202 36455
42467 88801  91280 01056  27534 81619  79004 25824  66362 33280
20706 31929  57422 18730  96197 22101  47592 02180  18287 82310
60430 59627  26471 07794  60475 76713  45427 89654  14370 81674
41246 98416  08669 48883  77154 09806  94015 60347  20027 08405
33150 27368  53375 70181  59431 66642

is the sum is the sum of two primes, or not!  If it is the sum of two primes,
then execute plan A.  If, on the other hand, it is not the sum of two primes,
go to plan B.

On Plan A, quadrillions of years from now simply arrange the collapse
parameters of our universe so that after the sentients have all had
infinite run time, our universe ends in such a way that the one-bit answer
"True" is embedded in the final limit curvature. It's fun to think about how
that actually works, there being no "last" baby-universe involved.

On Plan B---the case that the Conjecture is false---then spawn a new sub-
universe that instructs the new baby universe to consider the next number
which is 2 greater than the one above. And for them as well there is to
be a corresponding Plan A and Plan B.  As you can see by induction,
this may ultimately involve infinitely many nested baby universes.

The above number is really pitifully small (as are almost all numbers) and of
course didn't require much work to determine that yes, it is the sum of two
primes.

Now, do you suppose that the hyper-intelligences of the local cluster were
insulted by this request from the mother universe?  Or dismayed  that the
entire point of our existence had been to make a trivial computation?  Not
in the least, because millions of years earlier they had fully intended to do
the very same thing thing themselves if only they could figure out how.

With bated-breath---or whatever passes for bated-breath among hyper-
intelligences---the "subroutine call" to the baby universe was made. A tiny
little micro universe was born, grew, collapsed and died, all in less than a
second of local time. And as it died, it embedded The Answer to the final
quest around which our entire existence is predicated.  And in this way it
became known: Goldbach's Conjecture is... false!

Not only was the one-bit answer returned, but---as instructed---the number
on which it failed was returned as well. Unfortunately, this medium is too small
to record the answer. For it's a number larger than ten to the ten to  the ten to
the ten to the ten... , iterated altogether 42 times!

And that *was* the end of the story.