The Ulam Spiral http://serendipity.magnet.ch/hermetic/pns/pns.htm http://serendipity.magnet.ch/hermetic/misc/numcol.htm http://www.alpertron.com.ar/ULAM.HTM http://yoyo.cc.monash.edu.au/~bunyip/primes/primeSpiral. http://yoyo.cc.monash.edu.au/~bunyip /primes/primeSpiral.htm htm http://yoyo.cc.monash.edu.au/~bunyip http://yoyo.cc.mo nash.edu.au/~bunyip/primes/triangleUl /primes/triangleUlam.htm am.htm http://www.jcrystal.com/steenweber/!A"A/primes/jprim http://www.jcrystal.com/steenweber/! A"A/primes/jprime#.html e#.html $unchec% 'all primes( and chec% 'triangle numbers( or a breathta%ing graphic)* http://www.cs.unh.edu/~charpo+/,ro http://www.cs.unh.edu /~charpo+/,rogramming/,ostScript-pr gramming/,ostScript-primes/ imes/ http://ourworld.cs.com/ttpi# http://ourwor ld.cs.com/ttpi##01/inde2.htm3 #01/inde2.htm34s 4s Several Ulam-like spirals (with no credit) http://www.%ented.org.u%/ngl/r http://www.%ented.o rg.u%/ngl/roseacre-numeracy/ oseacre-numeracy/numbers5uares.ht numbers5uares.html ml http://www.%ented.org.u%/ngl/r http://www.%ented.o rg.u%/ngl/roseacre-numeracy/ oseacre-numeracy/inde2.html inde2.html There is currently no e2planation or the distinct diagonal lines which appear when the primes are mar%ed out along a particular 6s5uare spiral6 path. This was accidentally disco+ered by nuclear physicist Stanislaw Ulam while he was passing the time during during a boring lecture. lecture. http://www.maths.e2.ac.u%/~mwat%ins/7eta/ulam.htm Ulam and a couple o his colleagues programmed the Maniac 88 mainrame at Los Alamos to plot a s5uare spiral diagram o the integers up to #9 million. The diagonal prime pattern continued. Although this phenomenon has been studied somewhat so ar nobody6s been able to ma%e anything out o it $Homan*. http://www.google.com/search3 54cache:;
;g?:www.angelire.co 54cache:;;g?:www.angelire.com/ca@/Thechurch@/pr m/ca@/Thechurch@/primepape imepape r.nbB@@s5uarespiralB@@ulamChl4en
Biography http://www-groups.dcs.st-and.ac.u%/~history/Mathematicians/Ulam.html http://spot.colorado.edu/~gamow/george/#[email protected] http://www.aulam.org/stanulam.htm http://scienceworld.wolram.com/biography/Ulam.html E> 'the law o a+erages(: http://www.ma2+alue.com/news##.htm E> penchant or in+enting pattern games or the computer at Los Alamos: http://www.brunel.ac.u%/depts/A8/alie/al-ca.htm
“Fringe elements/Criosities! (not necessarily "or dissemination) aF Ulam interests the =ible ?ode crowd and or Gann the =ible is the greatest o all te2tboo%s: http://jollyroger.com/77/ychristiand/atchman>eehall/cas/I.html http://jollyroger.com/77/ychristiand/atchman>eehall/cas/1.html bF Ulam pops up in channeling session on music and the structure o pyramids both Gann areas o study: http://#0I.@D.J.#@D/cass/stephanie.htm cF Ulam is not directly mentioned but the site below suggests that nuclear weapons and speciically the H-bomb o which Ulam was the co-creator were de+eloped through crac%ing the sacred geometry o the Knights Templar. The coincidences with Gann are many three o which are:
#F 8 belie+e as recently posted to the 'Tunnel Thru the Air( group that Gann ma%es reerence to the Knights Templar in his no+el in '+eiled language.( @F En the site the author says: 'The =abylonian god being .A. or Eannes attired in his ish suit holds the bread and a pail or grail. According to the =abylonians he ounded ci+ili7ation on arth. He is also eatured in the scene on the right standing in ront o the ,illar.( hile in =oston recently 8 made a photocopy o a boo% which 8 'happened( to see and borrow rom the library when 8 was in graduate school many years ago illiam Simpson The !onah Legend: A Suggestion o 8nterpretationF. His position is that !onah is an initiatic story. And he has the same illustration o Eannes in the boo% and reerences in dierent places to Eannes. And i 8 were to turn anywhere or interpretation o Gann 8 would probably turn irst to anything Mason-related 8 could get my hands on.F 8t is stri%ing indeed that GannNs ;obert Gordon says “8 ha+e read the =oo% o !onah thru +ery careully and 8 belie+e that 8 understand what the Sa+iour meant when he said: O>o sign shall be gi+en but the sign o the prophet !onas.N 8 belie+e there was a secret meaning in what he saidP that the Son o man be three days and three nights in the heart o the earth. 8 belie+e that a man who understands the meaning o that has all the power nder heaven and earth as the =ible says he shall ha+e. 8 belie+e that that is the %ey to the interpretation o the uture. 8 am sure 8 ha+e ound it and %now how to apply it.( 'Tunnel( p. J1F 8s it possible to lin% !onah to Eannes3 8 so ';obert Temple $in The Sirius Mystery* ma%es a closely-argued case that Eannes and the Sirius connection is at the heart o the ?lassical Omystery religionsN that ha+e so ar deied e2planation because they were deliberately recorded in coded ormP initiates o the mysteries were orbidden to re+eal the arcane %nowledge they had been taught.( http://sphin2temple.+irtuala+e.net/articles/dogon.html F =oth Ulam and Gann were wor%ing with a number spiral or a s5uare o nine. Ulam was one o the co-in+entors o the H bomb and Gann had on his recommended reading list esley StoutNs Secret an '2planation E The ?reation C
,rinciples E Atomic eapons( Sacred Science catalogF. 8 e2amined the boo% while in =oston but 8 didnNt %now about Ulam then so 8 donNt remember 5uite honestly i it mentioned him by name. http://www.williamhenry.net/H-Bomb.htm
http://www.ama7on.com/e2ec/obidos/AS8>/#D19J111/
Bi#liography The ollowing reerences are boo%s or articles speci"ically related to the Ulam spiral$ Apostol Tom M. 8ntroduction to Analytic >umber Theory pp. J-I Qa+is ,hilip !. and Hersh ;euben The Mathematical 2perience Qembs%i illiam A. ;e+iew o ?rac%ing the =ible ?ode, First Things, >o. D0 pp. J#-J August/September #11D. Qembs%i illiam A. The Qesign 8nerence, ?ambridge Uni+ersity ,ress #11D. Qewdney A. K. RHow to pan or primes in numerical gra+elR Scientific American !uly #1DD p.19-1 see p. 1#F llerstein S. M. RThe ,ronic ;enaissance: The Ulam S5uare Spiral ModiiedFR Journal of Recreational Mathematics %& F Gardner M. The Si2th =oo% o Mathematical Games rom Scientiic American ?hicago 8L: Uni+ersity o ?hicago ,ress pp. D9-D and DD-D1 #1D. Homan ,. The Man ho Lo+ed Enly >umbers: The Story o ,aul rdos and the Search or Mathematical Truth >ew or%: Hyperion pp. #90-#91 #11D. ,ic%o+er ?liord A. ?omputers and the 8magination pp. @#-@#
REC the journal o computer mathematical recreation includes an article about a graphical display o prime numbers Stanislaw Ulam6s spiral. $;? 191 "iolet Terrace ?lar%s Summit ,A #D## USA* Satino+er !erey M.Q. ?rac%ing the =ible ?ode, illiam Morrow and ?o. >.. #11I Technical Appendi2 =. Stein M. L.P Ulam S. M.P and ells M. =. 'A +isual display o some properties o the distribution o primes.( American Mathematics Monthly. I# 0F: 0#J-0@9. See also: Sets >umbers and Uni+erses Selected or%s ?ambridge : The M8T ,ress #1I. J19-J10. J1DF The abo+e were culled rom the ollowing sites: http://[email protected]%/bnielsen/ulam.html http://www.maths.e2.ac.u%/~mwat%ins/7eta/ulam.htm http://mathworld.wolram.com/,rimeSpiral.html http://www.geocities.com/?ape?ana+eral/Launchpad/0##/[email protected] $search Ulam* http://www.%athryn%uhlman.com/codes/christm.htm c: http://home.earthlin%.net/~mcdemarco/portolio/elsmath.html The "ollowing are #ooks #y Ulam himsel"$ http://www.ama7on.com/e2ec/obidos/search-handleurl/inde24boo%sCield-%eywords4UlamB@?B@9Stanislaw B@9M/re4brsub/ http://www.ama7on.com/e2ec/obidos/AS8>/90@#J11/ http://www.ama7on.com/e2ec/obidos/AS8>/9#@1@#09I/ These are general re"erences on Ulam' not necessarily related to the spiral$
http://www-groups.dcs.st-and.ac.u%/~history/;eerences/Ulam.html
>ET Ulam but interesting: http://mcraeamily.com/MathHelp/,u77leSe5uenceES5uares.htm
