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 2018-09-02, 16:50 #1 hal1se   Jul 2018 3×13 Posts every exponantial ranges brun's sum: very slow go to low! http://www.britannica.com/science/twin-prime-conjecture In 2010 Nicely gave a value for Brun’s constant of 1.902160583209 ± 0.000000000781 based on all twin primes less than 2 × 10^16 0.000000000781 __123456789012 1,902160583209+0,000000000781= 1,90216058399 1,902160583209-0,000000000781= 1,902160582428 ** __12345678 8 digit after comma! range 2e16 to 1e17 real prime count:2075693725704225 ln(middle point of range)= =ln((2e16+1e17)/2)=ln(6e16)=38,633120957132785945100340633331 rough twin count= =1,3219*(2075693725704225/38,633120957132785945100340633331= =71023501804397 -+(%1) range first twin: (20000000000000129, 20000000000000131) range last twin: (99999999999998807, 99999999999998809) 99999999999998807=~1e17 99999999999998807 so 17 decimal digits, difference microscopic! for 1e17=10^18, so 18 decimal digits range_brun_sum > range_twin_count*(2*1/1e17) 0,001420=range_twin_count*(2*1/1e17) range_brun_sum=1/20000000000000129 + 1/20000000000000131 + ... + 1/99999999999998807 + 1/99999999999998809 range_brun_sum [newer less] range_twin_count*(2* 1/1e17) 71023501804397*2/1e17=0,001420 0,001420 __123 3th digit after comma :1 1,902160582428 ** __12345678 4. digit after comma not meanfull! so: 1,902 only true! if some one say, your calc. rough! not important rough! we use last range element:2*1/1e17 range_brun_sum > range_twin_count*(2*1/1e17) so, may be:0,001420 up to another great number! but 2. digit not wrong.(2. digit true only range 0 to 1e18) only 4. and may be 3. digit after comma false! range 1e17 to 1e18 range real prime count=22116397130086627 middle point of range=5,5e17 range rough twin count=1,3219*22116397130086627/ln(5,5e17)=715706232480603 -+(%1) 715706232480603*(2/ 1e18)=0,001431 if range rough twin count <%1 real twin count: 715706232480603*99/100=708549170155796 708549170155796*(2 /1e18)=0,001417 0,001431=~0,001417 near! not important %1 rough twin count! range 1e17 to 1e18:0,0014... same before 2e16 to 1e17 range 0,0014... this 0,0014s must be large number, so:this two range_brun_sums must be >0,0014.. range 1e18 to 1e19 range real prime count:209317712988603747 middle point of range=5,5e18 range rough twin count=1,3219*209317712988603747/ln(5,5e18)=6412256746480331 -+(%1) 6412256746480331*(2/ 1e19)=0,001282... stop! zem! this 3 range bruns' sum 0,001282+0,001417+0,00142=0,005539 0,005539 __123 after comma 3. digit: 5 0 to 2e16 sieve brun sum=1.90216... 1,90216058+0,005539=1,90769958 http://www.britannica.com/science/twin-prime-conjecture In 2010 Nicely gave a value for Brun’s constant of 1.902160583209 ± 0.000000000781 based on all twin primes less than 2 × 10^16 0.000000000781 __123456789012 12 or 8 digit only ilizione! dear Nicely! only 2 digit after coma true! 1,90 brun sum must be > 1,907 very clear! analysis brun sum: i am an autistic, brain damage! last day same one say: twin-prime-conjecture so i search at duckduckgo i saw brun's sum. this time analysis it: range: exp(n) to exp(n+1) for example: ____ 23 24 4,783989444169075e-03 1,79213361739538 this mean: range: int(exp(23)) to int(exp(24)) 4,783989444169075e-03 : this mean :range brun sum 1,79213361739538 : this mean 0 to range upper bound cumulative brun sum please forgive this paste, but please look every one this results: 1,5 hours test: 18 floating point variables but only 15 digit print out! ____ 0 1 0 0 ____ 1 2 ,8761904761904762 ,8761904761904762 ____ 2 3 ,279287276191301 1,155477752381777 ____ 3 4 ,1143868809927461 1,269864633374523 ____ 4 5 ,1137490813040892 1,383613714678613 ____ 5 6 8,872646653751062e-02 1,472340181216123 ____ 6 7 5,521056269861256e-02 1,527550743914736 ____ 7 8 ,0440171676677505 1,571567911582486 ____ 8 9 3,913401191595095e-02 1,610701923498437 ____ 9 10 2,808981294480608e-02 1,638791736443243 ____ 10 11 2,353587031749571e-02 1,66232760676074 ____ 11 12 1,982513665126122e-02 1,682152743412 ____ 12 13 1,675856631072195e-02 1,698911309722722 ____ 13 14 1,449627888590353e-02 1,713407588608626 ____ 14 15 1,268681390107178e-02 1,726094402509697 ____ 15 16 1,104899602949351e-02 1,737143398539191 ____ 16 17 9,708477915365204e-03 1,746851876454556 ____ 17 18 8,609915072354517e-03 1,755461791526911 ____ 18 19 7,720212327956113e-03 1,763182003854867 ____ 19 20 6,946011873574503e-03 1,770128015728441 ____ 20 21 6,28638488254902e-03 1,77641440061099 ____ 21 22 5,716112332965187e-03 1,782130512943955 ____ 22 23 5,219115007254201e-03 1,78734962795121 ____ 23 24 4,783989444169075e-03 1,79213361739538 only look every range sum please. for examle: 4,783989444169075e-03 how mean only this range sum? every exponantial range brun's sums very slow go to low! some one test million cores 128 bit computer, 38 floating point calculation, 0 to 1e29 for twins < 2^40 then clasic sieve and twins > 2^40 fast sieve, and even million cores and time > a few hundres years: sum result only after comma only 5. digit meanfull! may be: brun sum > 1,9, don't forget!
 2018-09-03, 07:18 #2 hal1se   Jul 2018 3·13 Posts every exponantial ranges, brun sum regularly! question: average reciproc element=avr? ____ 22 23 5,219115007254201e-03 :range brun sum range exp22 to exp23: real twin count:15957923 2*avr*real twin count=range brun sum avr=range brun sum/(2*real twin count)= 5,219115007254201e-03/(2*15957923)=1,6352739035193367582986833562237e-10 ln(reciproc(1,6352739035193367582986833562237e-10))=22,534040614533721383423945094182 ____ 23 24 4,783989444169075e-03 ln(reciproc(range brun sum/(2*real twin count)))= =ln(1/(4,783989444169075e-03 /(2*39772849))) =23,534322700912901121694938047962 ____ 21 22 5,716112332965187e-03 1,782130512943955 ln(1/(range brun sum/(2*real twin count)))= =ln(1/(5,716112332965187e-03/ (2*6427922)))=21,533775418648340934467457654403 ____ 13 14 1,449627888590353e-02 ln(1/(range brun sum/(2*real twin count)))= =ln(1/(1,449627888590353e-02 / (2*5472)))=13,534409930911060546669441893616 does see some one any mean? exp 13 to exp 14 avr=13,5+0,034409930911060546669441893616 exp 23 to 24 avr=23,5+0,034322700912901121694938047962 avr remainder diffrence exp13 and exp 23: 0,0344099-0,0343227=0,0000872 very low difference! exp 21 to 22 avr remainder: 0,03377541 avr remainder diffrence exp21 and exp 23: 0,0343227 - 0,03377541 = 0,00054729 low difference! but not very low! if twins in exponantial range windows, we see surprise regularly.
 2018-09-03, 07:20 #3 hal1se   Jul 2018 478 Posts 10^n range test up to n=11, range brun sum very slow go to small! question: if range 10^n, brun sum: this internet board many people, angry to me, for 'computer' print output, paste. if Nicely, before test 2*10^16, only first a few 10^n range test, only a few hours! He is see easly, this range brun sum very low go to small! ____ 0 1 ,8761904761904762 ,8761904761904762 ____ 1 2 ,4547998895286105 1,330990365719087 ____ 2 3 ,1870420978405043 1,518032463559591 ____ 3 4 9,886109387260966e-02 1,616893557432201 ____ 4 5 5,590602739554085e-02 1,672799584827741 ____ 5 6 3,797734597647975e-02 1,710776930804221 ____ 6 7 2,758011311304998e-02 1,738357043917271 ____ 7 8 2,045857715070371e-02 1,758815621067975 ____ 8 9 1,592033657056097e-02 1,774735957638536 ____ 9 10 1,274254508070533e-02 1,787478502719241 ____ 10 11 1,042580823589026e-02 1,797904310955131 range 10^10 to 10^11 range brun sum>1e-02 1e-02=0,01 if, i will explain temporary result brun sum: up to 10^11 1,797904310955131-+ bla bla is this result ethic? i must be say: brun sum > 1,79 up to 10^11
 2018-09-03, 09:36 #4 LaurV Romulan Interpreter     Jun 2011 Thailand 22·2,287 Posts continuing this crap, soon enough ye'll get your own blog and be restricted to blogorhea forum...
 2018-09-05, 23:07 #5 hal1se   Jul 2018 3910 Posts how method brun sum calculate easy? dear larry, please don't angry. patient please! if are you know 1e26 to 1e27 range brun sum lower limit, please calculate, and show me! but not read before bottom efore calculation! question: what is known, range brun sum lower limit? for this answer, step by step: question: big range twin count stabil? range:exp(35-+0,5) 961965785544776 2614894114445696 Prime numbers: 47119213510151 Twin primes: 1773579320354 Elapsed time: 2330556.63 sec ~ 27 days (my old amd 4 cores 1,6Ghz 8GB Ram laptop) ln(middle point of range): ln( (exp35,5 + exp34,5)/2 )=35,12011450695827752463176337351 ln: logarithm natural please look at this result: ts:twin stabil number: 1,32192 (only exp(n-+0,5), n>33) 1,32192*47119213510151 / 35,12011450695827752463176337351 = 1773565707224,4 1773565707224 : rough twin count. deviation:(1773565707224-1773579320354)/1773579320354=-7,6e-6 replace 1,32192 to 4/3, so:if we take 4/3, this rational number, only 0 to exp(35,5) rough twin count. but this time we look only high stability! range:exp(34-+0,5) 353887435612259 961965785544776 Prime numbers: 17842861844016 Twin primes: 691321034769 Elapsed time: 816749.49 sec ~ 9,5 days ln(middle point of range): ln( (exp33,5 + exp34,5)/2 )=34,12011450695827752463176337351 1,32192*17842861844016/34,12011450695827752463176337351 = 691288299282,6 691288299282 : rough twin count. deviation:(691288299282-691321034769)/691321034769=-4,7e-5 deviation negative: lower limit! deviation very low! range: exp(-+0,5+33) 130187912050633 353887435612260 Prime numbers: 6762467049487 Twin primes: 269934079037 Elapsed time: 480536.52 sec ~ 5,5 days ln(middle point of range):33,12011450695827752463176337351 0,1201145069582775246317633 : stabil! 1,32192*6762467049487/33,12011450695827752463176337351=269909708198,01 rough twin count=269909708198 deviation:(269909708198-269934079037)/269934079037=-9,028e-5 deviation: negative! this mean: lower limit! deviation very low!: this mean previous big ranges very small fluctation, so very stabil twin count! question: range 10^n windows twin count stabil? test: range 1e10 to 1e11: Primes: 3663002302 Twin primes: 196963369 Seconds: 24.877 1,32192*3663002302/ln(5,5e10)=195797764 deviation:(195797764-196963369)/196963369=-0,0059 deviation negative: lower limit! abs(deviation)<0,006, so <%0,6 test2:range 1e11 to 1e12: Primes: 33489857205 Twin primes: 1646209172 Seconds: 316.650 1,32192*33489857205/ln(5,5e11)=1637650668 deviation:(1637650668-1646209172)/1646209172=-0,0052 test3:range 1e12 to 1e13: if range goes to big ranges then abs deviation goes to very low numer! very important result! question:what is known, prime counting 10^n range: duckduckgo.com/?q=prime+counting+funtion first result: https://en.wikipedia.org/wiki/Prime-counting_function my zone bloc this internet type, but not important, i look tor browser easy: range: ral prime count: <10^26: 1699246750872437141327603 <10^27: 16352460426841680446427399 this is very important information for rough twin count: 1e26 to 1e27 range prime count: 16352460426841680446427399 - 1699246750872437141327603 = 14653213675969243305099796 rough twin count=1,32192*14653213675969243305099796/ln(5,5e26)= =314597359935696445388506 -+%1 (abs(deviation) may be only <%0,1 but we must %1, if some one count real twin, everybody sure!) =3,14597359935696445388506e+23 24 digit twin count! question: what is average reciproc element for 10^n ranges? 1e10 to 1e11 range: ____ 10 11 1,042580823589026e-02 :range brun sum. log(1/(range brun sum / (2* range twin count)))= log( 1/(1,042580823589026e-02 / (2*196963369)) )=10,5773 important:log mean base:10 logarithm! not this log mean, ln:logarithm natural. 10,5 + 0,0773 : this mean 0,0773 average brun sum reciproc remainder! if we take 2*0,0773=0,1546 lower limit range brun sum remainder. if we take negative: -0,0773 remainder, this time upper limit range brun sum. question: 1e26 to 1e27 range brun sum lower and upper limit=? very easy: range average reciproc remainder: 26,5 + 0,0773 = 26,5773 lower limit range reciproc element : 1/( 10^(26,5+2*0,0773) )=2,2151339841371935282722195619031e-27 lower limit brun sum=range twin count*(2* lower limit range reciproc element)= =314597359935696445388506*(2* 2,2151339841371935282722195619031e-27) =0,00139375 upper limit range reciproc element : 1/( 10^(26,5 -0,0773) )= 3,7783309865888608585373512944833e-27 upper limit brun sum=range twin count*(2* upper limit range reciproc element)= =314597359935696445388506*(2*3,7783309865888608585373512944833e-27)= =0,0023773 how mean this result? range 1e26 to 1e27 only for this range brun sum > 0,00139375 simple say: range brun sum > 0,001 this mean: cumulative brun sum up to 1e27, after comma 3. digit not meanfull! https://planetmath.org/BrunsConstant B=∑pp+2⁢ is prime(1p+1p+2)≈1.9216058 after comma digit? if we look exponantial range windows for brun sum, exp(87) to exp(88) range brun sum lower limit > 1e-6 5. digit not meanfull! exp(88)=1,6516e+38 up to 1e38, after comma 6. digit not stabil! question: how calculate this 7.digit? exp(88) to exp(89) rough twin count: (4/3)*exp(88,5+0,12011450695827752463176337351)/((88,5+0,12011450695827752463176337351)^2)= =5,2131574144461774557010443800843e+34 this twin count very rough! twin count must be > 1e34 even we use combiatric method this 1e34 * 2 times element, (1/(twin first prime) + 1/(twin first prime + 2) ) reciproc element sum how method? 2e34 sum only for this range: exp(88) to exp(89) if we can, 1e18 reciproc sum per second by super computer, 2e34/1e18=2e16 seconds=~2e16/3600/24/365=634195839 years. but 6. digit not stabil, up to exp(88). question again: https://planetmath.org/BrunsConstant B=∑pp+2⁢ is prime(1p+1p+2)≈1.9216058 how method after comma 7. digit? question: this brun sum calculate 10. digit, but not use computer, only windows calculator, only < 1 minute! answer: yes posible. don't angry larry please! only think larry please! how method brun sum calculate easy?
 2018-09-06, 04:17 #6 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 220558 Posts Welcome back, dear Raman!

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