Output this 1364-digit base-10 number:
10346063175382775954983214965288942351853612536382034663905935101461222060548195774084941504127779027795484711048746289269095513027910438498906751225648197766590064457965461314130149942152545074712074006545797623075756579902190433531325851645586375231773037880535184421903026638874897489950008250798014478066014893203193926076357920163707042852616942733354325378261468425502224936203089956427521668102778596882443702230532724374828028933960643144327285227754985461570358500265135333500954075465441985256254776102064625494398779453723330206306859677410408807692326906168737018862161148707729611012076342295413323680430446529763872458887191437347994063250920466184003173586602441075384748222102267773145003624260992372156354624662289026123081819214885321984526331716887191378907363723962768881646531494039722207338471537744184950666337656928147552391544567298663655079621129011773598162469141317639170063853667739680653118979048627652462235681893246541359880812508588104345141359691398313598202577424145658860334913269759048622492214169304247816441675958725602279911468750380291607080058491441201347157459047314438815796116358356171983789000270540329047696182295315977628397256525031861796294929740163865774776146472541890007191451515587790900275580657982495983198842069735835409348390389014043245596652434869311982404102985853034513631928339140603461069829946906350
This number is the entire text of the singularly elegant puzzle Ginormous by Derek Kisman from the 2005 MIT Mystery Hunt. It encodes a single-word message in a clever multilayered way for solvers to figure out without any instructions. You might want to try solving the puzzle before reading further.
How was this number produced? We reverse the steps from the puzzle solution. Since the solution performs repeated prime factorization, we produce the number by repeatedly multiplying specific primes derived from the previous step.
Start with the solution word
UNSHARPENED
and convert it to a list of numbers withA=1, ... Z=26
to get[21, 14, 19, 8, 1, 18, 16, 5, 14, 5, 4]
.Convert each number to a 5-digit prime where:
- the first two digits count up from 13
- the third and fourth digits are the numbers from the previous step, with a leading zero for one-digit numbers
- the last digit is the smallest one to make the whole 5-digit number prime
This gives:
13217 14143 15193 16087 17011 18181 19163 20051 21143 22051 23041
Find their product
58322536285290033985886806240808836417438318459
.Take the digits,
5, 8, 3, ...
and count up from 0 skipping that many values in between.- Skip 5 numbers after 0 to get 6
- Skip 8 numbers after 6 to get 15
- Skip 3 numbers after 15 to get 19
- ... and so on
This gives you:
[6, 15, 19, 22, 25, 31, 35, 42, 45, 54, 60, 63, 73, 74, 75, 79, 83, 93, 102, 108, 117, 126, 133, 142, 143, 150, 153, 158, 159, 168, 169, 178, 187, 191, 198, 203, 205, 213, 218, 222, 231, 235, 237, 246, 251, 257, 267]
Take the respective \$n\$'th highest-primes (the 6th prime is 13, the 15th prime is 47, ...) and multiply them
13 * 47 * 67 * 79 * 97 * 127 * 149 * 181 * 197 * 251 * 281 * 307 * 367 * 373 * 379 * 401 * 431 * 487 * 557 * 593 * 643 * 701 * 751 * 821 * 823 * 863 * 883 * 929 * 937 * 997 * 1009 * 1061 * 1117 * 1153 * 1213 * 1237 * 1259 * 1303 * 1361 * 1399 * 1453 * 1483 * 1489 * 1559 * 1597 * 1621 * 1709
to get:
142994592871080776665367377010330975609342911590947493672510923980226345650368095529497306323265234451588273628492018413579702589
Finally, take the digits
1, 4, 2, ..., 8, 9
and put them as powers of successive primes in the factorization \$2^1 3^4 5^2 \cdots 719^8 727^9\$ to get the final number:10346063175382775954983214965288942351853612536382034663905935101461222060548195774084941504127779027795484711048746289269095513027910438498906751225648197766590064457965461314130149942152545074712074006545797623075756579902190433531325851645586375231773037880535184421903026638874897489950008250798014478066014893203193926076357920163707042852616942733354325378261468425502224936203089956427521668102778596882443702230532724374828028933960643144327285227754985461570358500265135333500954075465441985256254776102064625494398779453723330206306859677410408807692326906168737018862161148707729611012076342295413323680430446529763872458887191437347994063250920466184003173586602441075384748222102267773145003624260992372156354624662289026123081819214885321984526331716887191378907363723962768881646531494039722207338471537744184950666337656928147552391544567298663655079621129011773598162469141317639170063853667739680653118979048627652462235681893246541359880812508588104345141359691398313598202577424145658860334913269759048622492214169304247816441675958725602279911468750380291607080058491441201347157459047314438815796116358356171983789000270540329047696182295315977628397256525031861796294929740163865774776146472541890007191451515587790900275580657982495983198842069735835409348390389014043245596652434869311982404102985853034513631928339140603461069829946906350