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Old 2019-03-25, 22:38   #34
a1call
 
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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.
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Old 2019-03-25, 22:52   #35
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Congratulations on re-inventing a slower version of the Mills process.
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Old 2019-03-25, 23:08   #36
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Is this what you are referring to?

https://en.wikipedia.org/wiki/Mills%27_constant
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Old 2019-04-01, 01:55   #37
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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.
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Old 2019-04-02, 23:25   #38
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Quote:
Originally Posted by a1call View Post
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)])])])])])])])])]
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Old 2019-04-05, 20:48   #39
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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.

Last fiddled with by a1call on 2019-04-05 at 20:55
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Old 2019-04-06, 04:49   #40
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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
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Old 2019-04-08, 20:03   #41
a1call
 
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"Rashid Naimi"
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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:
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Old 2019-07-21, 14:19   #42
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An OEIS falserial sequence:

https://oeis.org/A306601
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Old 2020-08-01, 21:23   #43
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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")

Last fiddled with by a1call on 2020-08-01 at 21:24
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Old 2020-08-02, 01:02   #44
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Quote:
Originally Posted by a1call View Post
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
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