20190717, 22:05  #1 
Jul 2018
39_{10} Posts 
twin prime count HOW very regularly?
exponantial special ranges, prime and twin prime count: int[exp(n)]n^8 to int[exp(n)]+n^8
n=32 : counts? range: exp(32)(32^8) to exp(32)+(32^8) primesieve q c1 c2 c4 c6 time s128 t3 7896296018268032**8 78962960182680+32**8 Primes: 68719534132 Twin primes: 2835414199 n=33 : counts? primesieve q c1 c2 c4 c6 time s128 t3 21464357978591633**8 214643579785916+33**8 Primes: 85236900427 Twin primes: 3410326616 question: twin prime count ? can it be estimated? 85236900427 / ((33*68719534132)/(32*2835414199))=3410358149 deviation:(34103581493410326616)/3410326616=9,2e6 qbasic64 program for batch file: OPEN "d:\ps\exp34to44.bat" FOR OUTPUT AS #1 DIM a AS _UNSIGNED _INTEGER64 PRINT #1, "echo ____" + "> exp34to44.txt" FOR q = 34 TO 44 PRINT #1, "echo exp(" + MID$(STR$(q), 2) + ") >> exp34to44.txt" a = INT(EXP(q)) PRINT #1, "primesieve c1 c2 c4 c6 time s128 t4 q " + STR$(a) + "" + MID$(STR$(q), 2) + "**8 "; PRINT #1, STR$(a) + "+" + MID$(STR$(q), 2) + "**8 " + ">> exp34to44.txt" NEXT CLOSE END REM end of file n=34 to 44 batch file, for cmd command line: echo ____> exp34to44.txt echo exp(34) >> exp34to44.txt primesieve c1 c2 c4 c6 time s128 t3 q 58346174252745434**8 583461742527454+34**8 >> exp34to44.txt echo exp(35) >> exp34to44.txt primesieve c1 c2 c4 c6 time s128 t3 q 158601345231343035**8 1586013452313430+35**8 >> exp34to44.txt echo exp(36) >> exp34to44.txt primesieve c1 c2 c4 c6 time s128 t3 q 431123154711519536**8 4311231547115195+36**8 >> exp34to44.txt echo exp(37) >> exp34to44.txt primesieve c1 c2 c4 c6 time s128 t3 q 1171914237280261237**8 11719142372802612+37**8 >> exp34to44.txt echo exp(38) >> exp34to44.txt primesieve c1 c2 c4 c6 time s128 t3 q 3185593175711375638**8 31855931757113756+38**8 >> exp34to44.txt echo exp(39) >> exp34to44.txt primesieve c1 c2 c4 c6 time s128 t3 q 8659340042399374439**8 86593400423993744+39**8 >> exp34to44.txt echo exp(40) >> exp34to44.txt primesieve c1 c2 c4 c6 time s128 t3 q 23538526683702000040**8 235385266837020000+40**8 >> exp34to44.txt echo exp(41) >> exp34to44.txt primesieve c1 c2 c4 c6 time s128 t3 q 63984349353005491241**8 639843493530054912+41**8 >> exp34to44.txt echo exp(42) >> exp34to44.txt primesieve c1 c2 c4 c6 time s128 t3 q 173927494152050099242**8 1739274941520500992+42**8 >> exp34to44.txt echo exp(43) >> exp34to44.txt primesieve c1 c2 c4 c6 time s128 t3 q 472783946822934630443**8 4727839468229346304+43**8 >> exp34to44.txt echo exp(44) >> exp34to44.txt primesieve c1 c2 c4 c6 time s128 t3 q 1285160011435930828844**8 12851600114359308288+44**8 >> exp34to44.txt REM end of file n=34 : counts? exp(34) Seconds: 2880.734 Primes: 105046920323 Twin primes: 4079295626 question: twin prime count ? approximate value: 105046920323 / ((34*85236900427)/(33*3410326616))=4079309656 deviation:(40793096564079295626)/4079295626=3,4e6 exp(35) Seconds: 3600.814 Primes: 128678584218 Twin primes: 4854234505 question: twin prime count ? approximate value: 128678584218 / ((35*105046920323)/(34*4079295626))=4854214930 deviation:(48542149304854234505)/4854234505=4,03e6 exp(36) Seconds: 4343.392 Primes: 156728004566 Twin primes: 5748119658 156728004566 / ((36*128678584218)/(35*4854234505))=5748130599 dev:(57481305995748119658)/5748119658=1,9e6 exp(37) Seconds: 5647.871 Primes: 189863714848 Twin primes: 6775131690 189863714848 / ((37*156728004566)/(36*5748119658))=6775197297 dev:(67751972976775131690)/6775131690=9,7e6 exp(38) Seconds: 7180.391 Primes: 228831310050 Twin primes: 7950932791 228831310050 / ((38*189863714848)/(37*6775131690))=7950772767 dev:(79507727677950932791)/7950932791=2,0e5 abs(dev)>1e5 but 2/(10**5) mini value. exp(39) Seconds: 9078.952 Primes: 274462036937 Twin primes: 9291718004 274462036937 / ((39*228831310050)/(38*7950932791))=9291886734 dev:(92918867349291718004)/9291718004=1,8e5 exp(40) Seconds: 12329.989 Primes: 327680132730 Twin primes: 10816086221 327680132730 / ((40*274462036937)/(39*9291718004))=10816044496 dev:(1081604449610816086221)/10816086221=3,9e6 exp(41) Seconds: 14655.309 Primes: 389508780389 Twin primes: 12543315601 389508780389 / ((41*327680132730)/(40*10816086221))=12543346411 dev:(1254334641112543315601)/12543315601=2,5e6 exp(42) Seconds: 20925.439 Primes: 461078345073 Twin primes: 14494524702 461078345073 / ((42*389508780389)/(41*12543315601))=14494538414 dev:(1449453841414494524702)/14494524702=9,5e7 exp(43) Seconds: 29125.672 Primes: 543637516493 Twin primes: 16692556020 543637516493 / ((43*461078345073)/(42*14494524702))=16692427846 dev:(1669242784616692556020)/16692556020=7,7e6 exp(44) Seconds: 39701.873 Primes: 638556198014 Twin primes: 19161347348 638556198014 / ((44*543637516493)/(43*16692556020))=19161448061 dev:(1916144806119161347348)/19161347348=5,3e6 question: if we have only twin count information, how can we find other twin counts? exp(39) twin count = 9291718004 then exp(42) twin count approximate how? 9291718004*42^6/39^6=14494529452 dev:(1449452945214494524702)/14494524702=3,3e7 another test: exp(32) twin count =2835414199 then exp(41) twin count approximate how? 2835414199*41^6/32^6=12543530214 dev:(1254353021412543315601)/12543315601=1,7e5 another test: exp(40) twin count=10816086221 then exp(37) twin count approximate how? 10816086221*37^6/40^6=6775175307 dev:(67751753076775131690)/6775131690=6,4e6 another test: exp(43) twin count=16692556020 then exp(36) twin count approximate how? 16692556020 * 36^6/43^6=5748137040 dev:(57481370405748119658)/5748119658=3,0e6 another test:exp(42) twin count=14494524702 then exp(88) twin count approximate how? 14494524702*88^6/42^6=1226321293360 another test:exp(44) twin count=19161347348 then exp(88) twin count approximate how? 19161347348*88^6/44^6=19161347348*2^6=1226326230272 two different approximate value. these values very near. if can you test exp(88)88^8 to exp(88)+88^8 twin prime real count, you must see: deviation < 1e4=1/(10**4) dear programmer, please make twin prime count for range exp(45) to exp(88) if you wonder and try upper values, you must see: abs(deviation) < 1e4=1/(10**4) exp(big) range, for example exp((10**12)**(10**12)) ranges HOW regularly? i feel, for big ranges regularly without calculation. question: twin prime count HOW very regularly? i am an autistic, i love number regularities. please forgive my words many mistake and not good fluent. my brain damage. disavantage: no! may be avantage. we look full picture, sometimes. please think: a few tips: for HOW question. in the special range:exp(n)n^8 to exp(n)+n^8, twin count compare: near other many due prime system: near: cousin prime count, near: sophie germain p, 2p+1 due prime's first prime count =~ twin prime count. sophie prime count %6 or % 8 bigger then twin prime count in every big exp ranges. fluctation %2,5(not:only p in the range), near: G=2*int[int[exp(n)] /6 ]*6 symetric goldbach due prime count (p+q=G, p and q symmetric all primes on point G/2,p and q in the range), near: G=2*int[int[exp(n)] /6 ]*6+2 symetric goldbach due prime count *2, near: G=2*int[int[exp(n)] /6 ]*6+4 symetric goldbach due prime count *2, so: (G mod 6=0 symmetric primes count) =~ (G mod 6=2 symmetric primes count)+(G mod 6=4 symmetric primes count) , this mean =~ : not exatly equal, % 10 fluctational! near: please select (n^8) times 2 randomize integer in the range and look: these two integer same time prime then count=count+1, randomize count*(2,64...) near twin count, near: please mixed 2*n^8 sequantial integer: in the range: exp(n)n^8 to exp(n)+n^8, mixed and mixed. and select two integer sequantial. these two integer same time prime then count=count+1,randomize count*(2,64...) near twin count, so posible come back randomize or not come back randomize: not important! this 2,64... a fix value, every big exponantial ranges! randomize due count and twin count rate: allways a fix value every big exponantial range: 2,64... so: prime system regular base randomize, so:axiomatic, so:predicitive, so:formulative. randomize: not gambling! if we look many big randomize integers, these type systems predictive. math very easy, if think simple, and step by step.  end of text 
20190718, 17:40  #2 
"Dylan"
Mar 2017
2×293 Posts 
Firstly, a suggestion: you may want to put your results in a table (in a pdf document, for instance) to improve readability (as it stands, the post is quite long and people won’t want to read all of it).
And secondly, per Tomas Oliveira e Silva, the number of twin primes have been calculated to at least 4*10^18 (about exp(42.833)). You want a twin prime count near exp(88), which is about 1.65*10^38. Yeah, I don’t foresee a calculation of that being feasible anytime soon. 
20190719, 05:33  #3  
Aug 2006
3×1,993 Posts 
Quote:


20190719, 10:35  #4  
Jul 2018
3×13 Posts 
Quote:
so: every 30 integer only 6 prime test. or 210k{...} (72)*(52)*(32)=15 probably twin so: 2*15/210 every 210 integer only 30 prime test:1/7, 30/210 * (2*88^8)=1,02752721373008e+15 primalize test exp(88)=~1,65e+38 39 digit primalize test only 3 milisecond (poor technic 2019), so: every second 333 primalize test. if we have 10e6 parellel processor then: each proc. only 2*88^8/10e6=719269049 integer so only 719269049/7 =102752721 primalize test. 1,02752721373008e+15 /10e6/ 333/ 3600=85,7 hours if we have 1e6 parellel processor then: 857 hours or 35 days if you can have optimal technic (so:not use poor technic) only a few femto seconds need. math must more groving for primalize test. Last fiddled with by hal1se on 20190719 at 11:03 

20190719, 13:31  #5 
Jul 2018
3·13 Posts 
https://alpertron.com.ar/ECM.HTM
please paste: x=10**38+6*10**37+5*10**36;x=n(x);c<=1000;x please press 'only evaluate' button 999 prime search only 2,5 or 3 seconds my very old AMD laptop. (chrome browser faster than other browser, about %250 fast) so every seconds average 333 prime:ok but this technic very poor! please think: how can we calculate, faster 1e8 or may be 1e16 times. 
20190802, 19:54  #6 
Jul 2018
3×13 Posts 
partial look and look: all
if we wonder: twin system how like randomize, how different randomize?
please take two randomize integer in this range: int(exp(44))44^8 to int(exp(44))+44^8. and look: two integer, same time primes than count=count+1 44^8 times loop please. question: count=~? answer: count * 2,64 =~ twin prime count. question: twin prime system how different randomize test system? answer: if we look partial test result: twin system different randomize test? for example: randomize test may be sometimes: 1e5 times no appear same time two prime: but twin system: sequantial 1e5 integer no twin imposible, because: maximal twin gap < 44*44*44/1,32032=~64518 ln( exp(44)+44^8 )=44,00000109311=~44 so, if we look all integers in the range: twin gap > 65000 integers imposible! but 100000 sequantial randomize, same time no appear two prime may be posible, sometimes! quesion: twin prime system how like randomize test system? answer: if we look all test result: twin system count near randomize test*2,64 
20190804, 18:12  #7  
"Dylan"
Mar 2017
2×293 Posts 
Quote:
Assuming I understand you correctly, I created a Mathematica notebook to test this out (see attachment). However, due to timing constraints (I came to an estimate of 9.7 years to run the entire program), I ran the loop for 100 million iterations and then extrapolated to get the twin count. I then compared that to primesieve 7.4 and the number I got was less than 1% off the primesieve value. So in this case your idea makes sense. Some questions I have though: 1. Does this work for larger n than 44? 2. Continuing on this question, what is the asymptotic behavior of doing this if we replace 44 with n and let n go to infinity? Do we get the actual twin prime count, or does it diverge (and if so, does it grow or shrink relative to the actual value)? 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
find very easy twin prime in the infamy twin primes  hal1se  Miscellaneous Math  13  20181105 16:34 
small prime gap, regularly?  hal1se  Miscellaneous Math  12  20180827 13:40 
Highest Prime is also a twin prime... NOT  hydeer  Lone Mersenne Hunters  9  20180403 22:54 
Twin Prime Days, Prime Day Clusters  cuBerBruce  Puzzles  3  20141201 18:15 
Prime count up  henryzz  Lounge  7  20070919 19:45 