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 2019-03-25, 22:38 #34 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2·7·139 Posts A few pointers: The 36716 dd Falserial mentioned in post number 30 can be constructed from the following notation: Code: ø(1011698[102008(42256[1203(1206[704(580[219(16[79(6[9(5[2(1[3])])])])])])])]) Which lists the seed prime 3 and the multiples in each iteration that will yield a Prime at that iteration. Every iteration will roughly double the number of decimal digits of the previous iteration hence 36716 dd after 15 iteration from the 1 dd seed. The fact that a prime is of the Fulsorial format, is sufficient info (given that there are no very large multiples) to reconstruct the structure of the prime and hence prove it prime.
 2019-03-25, 22:52 #35 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2×4,591 Posts Congratulations on re-inventing a slower version of the Mills process.
 2019-03-25, 23:08 #36 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2×7×139 Posts Is this what you are referring to? https://en.wikipedia.org/wiki/Mills%27_constant
2019-04-01, 01:55   #37
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

2×7×139 Posts

The following 73431 dd Falserial has been proven Prime using PFGW:

Code:
ø[46657(1011698[102008(42256[1203(1206[704(580[219(16[79(6[9(5[2(1[3])])])])])])])])]
Please see the decimal expansion in the attached text file.
Attached Files
 CRQ-100-A-73431 dd Falserial By Rashid Naimi - Proven Prime using PFGW.txt (72.0 KB, 49 views)

2019-04-02, 23:25   #38
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

2×7×139 Posts

Quote:
 Originally Posted by a1call The following 73431 dd Falserial has been proven Prime using PFGW: Code: ø[46657(1011698[102008(42256[1203(1206[704(580[219(16[79(6[9(5[2(1[3])])])])])])])])] Please see the decimal expansion in the attached text file.
Missing a multiplier. the corrected notation:

Code:
ø[46657(1011698[102008(42256[1203(1206[704(580[219(16[79(6[9(5[2(1[1(3)])])])])])])])])]

2019-04-05, 20:48   #39
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

2·7·139 Posts

I input the wrong seed prime and ended up with a slightly larger prime rather than doubling the dd.

The following 73431 dd Falserial has been proven Prime using PFGW:

Code:
ø[56756(3013[102008(42256[1203(1206[704(580[219(16[79(6[9(5[2(1[1(3)])])])])])])])])]
Please see the decimal expansion in the attached text file.
Attached Files
 CRQ-110-A-73431 dd Falserial By Rashid Naimi - Proven Prime using PFGW.txt (72.0 KB, 51 views)

Last fiddled with by a1call on 2019-04-05 at 20:55

 2019-04-06, 04:49 #40 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2×7×139 Posts An inefficient nested Falserial-Prime decoding code. Inefficient, because I can't figure out how to use the Pari-GP forvec loop. Code: \\\\CRX-100-C - Nested Falserial-Prime Decoding Code by Rashid Naimi codeTitle="\n**** CRX-100-C - Nested Falserial Decoding Code by Rashid Naimi\n" \o1 decodeFalserial(p)={\\\\\\\\\\\WIP factorLimit=19^6; theString1 =Str("f"); theString3=Str(""); runningP = p; runningN = runningP-1; theCounter=1; while(runningN>1, theCounter=theCounter+1; for(k=1,factorLimit, if(runningN/k==runningN \k, if(runningN/k==sqrtint(runningN/k)*(sqrtint(runningN/k)+1), runningP = (sqrtint(runningN/k)+1); runningN = runningP -1; if(theCounter/2==theCounter\2, theString1 =Str(theString1, "[",k,); theString3=Str(theString3,"]"); , theString1 =Str(theString1, "(",k,); theString3=Str(theString3,")"); ); next(2); ); ); ); ); if(theCounter/2==theCounter\2, theString1 =Str(theString1, "[",runningP ,); theString3=Str(theString3,"]"); , theString1 =Str(theString1, "(",runningP ,); theString3=Str(theString3,")"); ); print(codeTitle,theString1,theString3); print("P",length(Str(p)),"\n\n"); } \\\\\\\\\\ decodeFalserial( 33613673608134979085133852727908890249762704277706896423054596633446844945409458043115108274976243854453682450912015064987747311743217117030453639615921912561272515053768003632718659309799856909162169913687841339940779186884127782271843686875610984912343095330326155431251054623489375481384493622064760301570926644939237166720928787305748559734824460005528043393084876547459434457213760243267167298865944876954072924582210062508575806756956496224256960965289759103067073509723233823713811451908062888168308530752133119807938172330348335142821476071600139412884669693999492171660419058346532474623398922511406150272251085715587005861683453981403973919763170914594345511848087062353082007565352624562378021842343128490791291789323318594201218848560147515180387445739169053103085068321042545287667919118807036314824491979827095249653817217522463558195211394347401932349257651148894794898006744180222640672307676279479444469009213045330197759014337894895969882191677630863427959232525754727401949281471046146613822653935443061738382250668092008800899911217514266681167047356338694935693335896841338719154402550956757632564245384163916546947350812820269405748979118424392031778943596117478726000882478494890665331970246484302092789605612155491133792505298936208409951153641168433030656627049132468671491040539167217353280751467930562702532372001676049604207890394151650475335391200634286517027148720697603661653488394444673502778895070668328621988165204953736748969518538858549087693898776410513655176294547404698371031661428444730338246667546451423696096898888090330920763395084900006282913667473817019479458572966692181102022332700203073508141431873475328020122495242656949176397826930573977356992929802274081390144821469751236270413579355700098412434712351538665974466932257806484422272837727241026162798247038727714905290264948696919241858081603030729045965004215178030538410166006987056591987512038811378565830705344838218737721405841749682202862076655368039785671661048949065061994672384653312240626911302961728325298588870295637147731150025537389627960644184774449274075165285983008919976543219183210735434410786875726748839134121414808437124567125652792224032497884179960405385965916073171443498024439068977997429048998198507980240783644010424396458934971621781614212005089205393192945404266673809562402802909068770048715925013672363760403745180540303939664281177681358458195995203154066554854946063806918863380289898004203690710540769374512272566175354686187603615147804741037688574020618262006831535775401284900424474078610333767849094516554032478474674523649211329467026133416103123304974723742047334366533433297963569432392928746937293173632034751058287827252539951381330653639511761746194558813726813273399710944158182427743957756517098484433506195553513981962605397175860598747417583751313876476139995767713496098177452975298797805457896285252848319106366451992951659938235451212025674736715299702009607289925839067950099790397931530545999774287704792476289977838394256886946831765196777552587583963794996470625191900062699531672637113135653864013216331460516289764699657278555269525257967921996818775134915791095358928607778734087994026857780718001625749077382748697236996235870552329141759004743779458517778963067710646530998829412346874555352658177458198325990216909999479329961313907205784239584866182199410385728764707771475930068119900658992013635225744563649238975293844307202301628997977600402456679740121077307930573747424380974851649397464533729818944398318894408530990548316478279097276908634400317459905749736163449235354516296896296142367676520624568681335651266326525812531687488728709856851120739266121682604723572389225398096799427614423280020146398576481970083424847764537278773099721233900009725693388168718012805252324960004789629487118375252919695313404967487486662019697370764167725000684690252777503072103182314694001706412732358184931137638179396382615923911838658089362606875486381517503677095797349106501005365643674464987642954031502357092085151674808172273990993514179105466520659413170852722543975767274107635821609662153250527881110981157371902627221117464371824528195009492565060609102815342908736300966282860166024790042522068103805884929022006447154194059232336804615664299376943616397027838744165533167661125603748992130580025449499041498774658902589012843693642166453286202312760381466714986443492444668559384506223903096765268094979076951920925404386942910430238729887829566457821445097617597742739332923378899611311730931464754738246461640721181934305604514821264151395036407817358419450387026234388139964392780978884762008789095980445351150597362502661559213259141202500218285793324363621440058484125918680932319878250897480141918974196567356806487173848301016459663723648393626372804250338895269913768004629455032801292994120758562028021983155361937649465355692941471710226841241372598645312153041782904192973372719562413030884721761868392122937754439013208144327981726544453027057368806021099710485067684449042198017217687730560357834601942407058301513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) ## Output: Code: **** CRX-100-C - Nested Falserial Decoding Code by Rashid Naimi f[1011698(102008[42256(1203[1206(704[580(219[16(79[6(9[5(2[1(1[1[2])])])])])])])])]] P36716 (01:45) gp > ## *** last result computed in 1min, 8,890 ms. Last fiddled with by a1call on 2019-04-06 at 05:46
2019-04-08, 20:03   #41
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

2×7×139 Posts

The following 146866 dd Falserial has been proven Prime using PFGW:

Code:
ø[9146(56756[3013(102008[42256(1203[1206(704[580(219[16(79[6(9[5(2[1(1[1>2<])])])])])])])])])]

Please see the decimal expansion in the attached text file:
Attached Files
 CRQ-120-A-146866 dd Falserial by Rashid Naimi - Proven Prime using PFGW.txt (143.7 KB, 58 views)

 2019-07-21, 14:19 #42 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2·7·139 Posts An OEIS falserial sequence: https://oeis.org/A306601
2020-08-01, 21:23   #43
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

2·7·139 Posts

The 19th term was added to A306601

P242682 is verified to be Prime deterministically by adding the previous iterations to the helper file.

Code:
\\\\Pari-GP code to generate the Decimal-Expansion:
k = [1, 1, 2, 4, 8, 16, 5, 360, 142, 104, 34, 1904, 3127, 253, 1219, 8755, 16222, 7672, 22515]
p = 3
for(i=1, #k, p = k[i]*(p-1)*p-1)
print("\n",p,"\n")
Attached Files
 DMA-100-A-A306601-121339 dd Falserial by Rashid Naimi - Proven Prime using PFGW.txt (237.5 KB, 30 views)

Last fiddled with by a1call on 2020-08-01 at 21:24

2020-08-02, 01:02   #44
JeppeSN

"Jeppe"
Jan 2016
Denmark

2·34 Posts

Quote:
 Originally Posted by a1call The 19th term was added to A306601 P242682 is verified to be Prime deterministically by adding the previous iterations to the helper file.
Cool. The next one can be relevant for the Top 5000 of the Prime Pages (Caldwell). /JeppeSN