

P r i m e 


G o l d b a c h 
P r i m e G o l d b a c h 
Box23
save Upper Left graph

Box24
save Upper Right graph

Box25
save Lower Left graph

Box26
save Lower Right graph

P r i m e G o l d b a c h 
Box33
save Upper Left graph

Box34
save Upper Right graph

Box35
save Lower Left graph

Box36
save Lower Right graph

P r i m e G o l d b a c h 
<a name="docA001"> 201606211052 start 20160616 Liu,Hsinhan begin write prime number program http://freeman2.com/prime_e1.htm upload 20160623 prime_e1.htm is better than earlier http://freeman2.com/jsprime2.htm upload 20090915 prime_e1.htm has following control buttons. <a name="docA002"> Build prime number list and display defined prime at box01.
<a name="docA003"> 201606211111 here When open prime_e1.htm, program auto define prime from 2 to 5000 and display next message. Default:Program has 670 primes, from 2 to 5003 User can build prime to longer list. First fill a number in next click ASK⇒ message line show Build: Program has 348514 primes, from 2 to 5000011 To save time, program do NOT display prime table in Box01. User can ask program display current defined prime by clicking <a name="docA004"> Build prime list take few seconds time (Acer computer Aspire 5750Z4830) User can copy from other source and paste existing prime list to Box01, click When click [Update], program read box01 value and save to primeArr[] future calculation will base on user's data. It is user's responsibility to supply correct prime table (start from 2) prime_e1.htm do not check this table is correct or not. User can do on purpose, supply wrong list and update to primeArr[] see what happen if prime table is wrong. To erase wrong table, click , program define 2 to 19. You need click to create longer list. 201606211131 here <a name="docA005"> Box02 is main input and Box03 is main output .Box02 ; Default:Program has 670 primes, from 2 to 5003
<a name="docA006"> 201606211148 here Box02 is input box, example input look like [[ 8 9 10 14 15 16 20 21 22 38 39 40 ..... ]] <a name="docA007"> If gap=4 click Box06 output above list. prime pair (13,17) has gap=4 and (13,17) squeezed (14,15,16), put squeezed list to Box02 and click RUN ☞ get [[ 8=2^3 9=3^2 10=2^1 * 5^1 14=2^1 * 7^1 15=3^1 * 5^1 16=2^4 20=2^2 * 5^1 21=3^1 * 7^1 22=2^1 * 11^1 38=2^1 * 19^1 39=3^1 * 13^1 40=2^3 * 5^1 ..... ]] <a name="docA008"> Same input, if click get [[ 8=2*2*2 9=3*3 10=2*5 14=2*7 15=3*5 16=2*2*2*2 20=2*2*5 21=3*7 22=2*11 38=2*19 39=3*13 40=2*2*2*5 ..... ]] This utility help you analyse if prime gap=4, the squeezed number pattern. prime_e1.htm allow prime gap=any even number. <a name="docA009"> Why ASK⇒ ? When program has Default:Program has 670 primes, from 2 to 5003 if click example fill 82003/50773 to Box02 and click get [[ 82003= 50773= ]] Because both are prime and greater than 5003. In this case, click add more prime to list solve problem. 201606211216 here <a name="docA010"> When program has Default:Program has 670 primes, from 2 to 5003 if click example fill 1512890160007 to Box02 and click get [[ 1512890160007=1229993^1 * 1229999^1 ]] Program auto build prime table to cover needs. <a name="docA011"> Auto build or not auto build, program exam sqrt(1512890160007), if sqrt(1512890160007) is greater than table maximum prime then auto build. sqrt(1512890160007)=1229995.9999963415 > 5003 example auto build. but sqrt(82003)=286.36 < 5003 example user build. Auto build or not auto build, if program exam 1512890160007 and build a table cover 1512890160007 it takes many hours. Liu,Hsinhan choose program exam sqrt(1512890160007) not exam 1512890160007. Because program has auto build prime table action, is needed. 201606211232 here <a name="docA012"> 201606211522 start Box04 and Box05 click buttons are nextBox04 box allow you compare two similar data in box03 and 04
<a name="docA013"> 201606211533 here Box04 to Box05 main job is . Box04 input example is [[ 90=2^1 * 3^2 * 5^1 91=7^1 * 13^1 92=2^2 * 23^1 93=3^1 * 31^1 94=2^1 * 47^1 95=5^1 * 19^1 96=2^5 * 3^1 ]] <a name="docA014"> Box05 output example is next [[ 2 : 9 //prime 2 show up 9 times 3 : 4 //prime 3 show up 4 times 5 : 2 //same as above 7 : 1 11 : 0 13 : 1 17 : 0 19 : 1 23 : 1 29 : 0 31 : 1 37 : 0 41 : 0 43 : 0 47 : 1 ]] <a name="docA015"> Box04 input must use power expression. 90=2^1 * 3^2 * 5^1 is accepted Multiplication expression 90=2*3*3*5 do not work. Because code depend on '^' to find how many 3 and how many 5. <a name="docA016"> Box04 all numbers like "3^2" are considered. In other words, Box04 input represent what goal? squeezed numbers between (13,17) ? 14,15,16 numbers between (127,131) and (163,167) two fourgap prime set? 132,133,.....,161,162 Plain continuous integers 101,102, ... 199,200? These consideration are user's decision. summarize ALL "3^2" type numbers in Box04. <a name="docA017"> After write code, LiuHH paid attention that Box04 and Box05 set should shift to Box03 and Box04 set. Because Box03 output just 90=2^1 * 3^2 * 5^1 Later LiuHH did not shift, but add one line allow you compare two similar data in box03 and 04 If user has two similar power expression factorized integer numbers put side by side, it is easier to compare. 201606211559 here<a name="docA018">
<a name="docA019"> 201606211735 start Box06 and Box07 generate prime related integers. Input is Double prime gap This yellow box accept even numbers only. Start from 3 all prime are odd numbers. gap2 prime pairs are (3,5), (827,829) etc. gap4 prime pairs are (7,11), (379,383) etc. gap6 prime pairs are (23,29), (557,563) etc. gap8 prime pairs are (89,97), (683,691) etc. gap100 prime pairs are (396733,396833) and (4783873,4783973) etc. <a name="docA020"> Input number 8 for example to yellow box. Use Program has 670 primes, from 2 to 5003 for test run. Because following buttons work cover primeArr[] array WHOLE RANGE. Too big array, wait longer time. If current is long Program has 348514 primes, from 2 to 5000011 Click change to then click , make sure see Build: Program has 670 primes, from 2 to 5003 You can work faster. <a name="docA021"> Click button , output to Box06 the next [[ 90 91 92 93 94 95 96 360 361 362 363 364 365 366 ..... ]] <a name="docA022"> Gap8 primes are (89,97), (359,367) etc. (89,97) squeeze 90,91,92,93,94,95,96 . (359,367) squeeze 360,361,...,365,366 . Box06 list those squeezed numbers. Click send data to Box02. Next click study factorization pattern. <a name="docA023"> Below Box06 click button Box06 and Box07 both output answer. Box06 has next [[ 89,97 359,367 389,397 401,409 449,457 479,487 491,499 683,691 ..... ]] <a name="docA024"> Box07 has next [[ 97,359 367,389 397,401 409,449 457,479 487,491 499,683 691,701 ..... ]] <a name="docA025"> Box06 output (89,97), (359,367) they are gap8 pair. Box07 output (97,359), (367,389) they are gap8 pair outsider bounds. If someone want study gap8 pair outsider numbers. Bounds are in Box07. If you want study gap8 pair outsider numbers between 499,683 . Copy and paste 499,683 to Integer ends Replace 101,200 with 499,683 then click and click . Continue Box02 procedure. <a name="docA026"> Below Box06 click button Box07 output [[ Double MIDDLE, gap=8. Number +/4 are prime numbers. 93 363 393 405 453 483 495 ..... OUTSIDEgap MIDDLE, gap=8 228 378 399 429 468 ..... ]] gap8 first pair is (89,97), its middle is 93. gap8 2nd pair is (359,367), its middle is 363. gap8 3rd pair is (389,397), its middle is 393. (89,97) to (359,367) middle point is (35997)/2+97=228 which is OUTSIDEgap MIDDLE generate all middle numbers, help user analysis. <a name="docA027"> Below Box06 click button follow , that is click first, second. work with green box Output choice Green box read yellow box value. If Double prime gap has value 8, then green box choice from 1 to 7. Click green box, box value change below 8. <a name="docA028"> then gap8 prime pairs 89,97 ; 359,367 ; 389,397 ; 401,409 ; 449,457 squeezed numbers are 90, 91, 92, 93, 94, 95, 96 360,361,362,363,364,365,366 390,391,392,393,394,395,396 402,403,404,405,406,407,408 450,451,452,453,454,455,456 etc If green box has number 2 , click [squeezed number] then [squeezed middle] all second number recorded in Box06. They are 91,361,391,403,451,481,493 ... <a name="docA029"> move Box06 output to Box07 output to Box06 the next [[ 90 91 92 93 94 95 96 91 361 391 403 451 481 493 685 703 721 745 763 913 931 985 1111 1165 1195 1375 1441 1525 1561 1573 1735 1825 1981 2005 2155 2215 2245 2275 ..... ]] <a name="docA030"> Top seven number is first squeezed set 90,91,92,93,94,95,96 The following numbers are NOT a whole set. The following numbers are second number in each set. First few are 91 361 391 403 451 ..... This function help reader study each gap8 second number has what pattern. Initially, LiuHH paid attention to middle only. No choice, later think it is easy to add choice code. <a name="docA031"> Below Box06 click button If yellow box has value 8. output to Box06 the next [[ 88 <== outsider 89 <== prime 90 91 92 93 <== squeezed middle 94 95 96 97 <== prime 98 <== outsider 358 <== outsider 359 <== prime 360 361 <== squeezed 362 363 364 365 366 367 <== prime 368 <== outsider ..... ]] <a name="docA032"> [squeezed+prime] is actually squeezed+prime+twoNeighbor LiuHH just hope see prime factorized numbers what pattern they have. For example gap8 middle they all have factor 3. gap10 middle they all have factor 6. gap12 middle they all NOT have factor 6. These observation do not help much. a506231921 Liu,Hsinhan did not see any exciting pattern. prime_e1.htm is online If many scholar study prime pattern, there are greater chance find exciting pattern. <a name="docA033"> Now http://freeman2.com/prime_e1.htm is in your hand. If you want to analysis prime factorized numbers, prime_e1.htm is a tool you can use. As usual No one proofread Liu,Hsinhan work No one test run Liu,Hsinhan program. This file may contain error. Reader must use prime_e1.htm with caution. Liu,Hsinhan 劉鑫漢 201606211942 stop <a name="docA034"> 201606212222 start 201606212210 LiuHH run (Build spend 30 seconds) Build prime list up to 20000000 Build: Program has 1270608 primes, from 2 to 20000003 Double prime gap 100 Double MIDDLE, gap=100. Number +/50 are prime numbers. [[ 396783=3^2 * 44087^1 838299=3^1 * 7^1 * 11^1 * 19^1 * 191^1 1313517=3^1 * 41^1 * 59^1 * 181^1 1648131=3^1 * 83^1 * 6619^1 1655757=3^2 * 183973^1 ..... 19294473=3^1 * 11^1 * 17^1 * 163^1 * 211^1 19304217=3^3 * 714971^1 19416561=3^1 * 6472187^1 19871331=3^1 * 37^1 * 179021^1 19917117=3^3 * 11^1 * 67061^1 ]] all middle have factor 3, no factor 2. 201606212228 stop <a name="docA035"> 201606292105 start Update 20160701 added Goldbach conjecture 201606190953 Liu,Hsinhan access http://www.ijpam.eu/contents/2013841/3/3.pdf [[ As is known, on June 7, 1742, Christian Goldbach in a letter to Leonhard Euler, Goldbach argued that, every even natural number greater than 4 can be written as a sum of two primes, namely: 2n = p + q, where n > 2, and p, q are prime numbers. ]] Liu,Hsinhan added a Goldbach section Box10, Box11 and Box12. Goldbach section has next structure.<a name="docA036">
<a name="docA037">
201606292135 here
Why need
Odd number  odd prime= white box number end with ';' or not?
Goldbach conjecture say that
Every even integer ( ≥ 6 ) is the sum of two odd primes;
Every odd integer ( ≥ 9 ) is the sum of three odd primes.
In fact odd integer ride on even integer. Because
subtract a prime 3, odd integer 25 become even 22,
subtract a prime 5, odd integer 25 become even 20,
subtract a prime 7, odd integer 25 become even 18,
subtract prime 11 , odd integer 25 become even 14.
Larger odd integer, more alternative choice it has.
<a name="docA038">
Program can force all odd integer subtract prime 3
But this Odd number  odd prime= box allow user
decide what prime number be a factor of odd integer.
If user assign 19 to white box. All odd integer in
Box10 will have 19 as a factor. If input Box10 has
odd integer 15, which is less than 19. Program use
3 as a participate prime.
201606292207 stop
<a name="docA039">
201606301005 start
If user input 29 to and in
Box10 Prime sum random input
assign numbers they are both greater than and less
than 29. Number 35 subtract user assigned prime 29
get 3529=6 The even integer 6 is just enough for
Goldbach split to sum of two primes that is 6=3+3.
<a name="docA040">
Odd integer 35=3+3+29 satisfy Goldbach conjecture.
Other odd integers in Box10 have trouble.
Odd integer 33 subtract 29 get 4 Four is less than
Goldbach requirement six.
Odd integer 21 subtract 29 get 8 Negative number
is not a concern in integer prime summation
decomposition analysis. For this consideration.
If user input prime P0 in white box and
input odd integer I0 to Box10.
If I0>=P0+6 I0 decomposition include P0.
If I0< P0+6 I0 decomposition include prime 3.
201606301032 here
<a name="docA041">
White box and are different.
201606301040 cannon shock.
201606301041 cannon shock.
If prime 3 in white box follow a ';', then Box11
output
[[
34=31+3
34=29+5
34=23+11
34=19+0 <== no match line
34=17+17
35=31+0 <== no match line
35=29+3+3
35=23+0 <== no match line
35=19+13+3
.....
]]
<a name="docA042">
';' in white box, bring "<== no match line "
to Box11. This is valid for both
and
201606301049 here
<a name="docA043">
Box10 is input box for
Integer upper/lower bounds is input
box for
read Box10 value and change integer
to sum of two prime or sum of three primes.
Box10 value allow random order integers.
read silver color box value. Need two
integers. One begin number, one end number. Code
in click button send sequential integers to Box10
and send prime summation decomposition answer to
Box11.
Integer prime multiplication decomposition is unique.
Integer prime summation decomposition has multiple
answers.
<a name="docA044">
Integer upper/lower bounds number end
with ';' or not , program behave differently.
If no ';' in Click
Box10 and Box11 output odd integer and even integer.
If in has ';' Click
Box10 and Box11 output even integer only.
Silver box has ';' or not only read
silver box. NOT read silver box.
201606301100 here
<a name="docA045">
201606301432 start
Below Box11, there is a click button
This button input from silver box, output to Box11
and Box12. Assume silver box has [6,20],
send number sequence to Box10.
[[
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
]]
<a name="docA046">
function GoldbachCount(arg1) receive above input
numbers. For even number GoldbachCount(arg1)
do prime multiplication decomposition and
do prime summation decomposition. For example
22=2*11 //prime multiplication decomposition
22=19+3 ; 22=17+5 ; 22=11+11 //summation decomp.
<a name="docA047">
output to Box11
[[
6, 1,1,1
8, 1,2,1
10,2,3,0
12,1,2,1
14,2,3,1
16,2,4,0
18,2,4,1
20,2,4,2
]]
All odd number in Box10 ignored in Box11. Because
odd number prime summation decomposition is just
replay for even numbers. No need repeat.
<a name="docA048">
Box11 "14,2,3,1" line say
Input number 14 prime summation decomposition
14=13+0 <== inactive equation, one prime 13
14=11+3 <== active equation, two primes 11,3
14=7+7 <== active equation, one prime 7
14 has 2 active equations 3 active primes 11,7,3
14 has 1 inactive equations 1 inactive prime 13
above
14=13+0 is inactive equation, because 13 cannot
sum any other prime to get 14.
Inactive equation count is same as inactive prime
count.
<a name="docA049">
Box11 has four columns, left most is input number.
Box12 has three columns, left most is prime number.
Box12 output next
[[
2:0,15
3:7,4
5:6,2
7:6,1
11:3,0
13:3,0
17:1,0
]]
<a name="docA050">
Box12 line "7:6,1" say the following
Input Box10 all EVEN numbers
prime summation decomposition prime 7 has 6 count.
prime multiplication decomposition 7 has 1 count.
Below Box04, click button do not refuse
odd numbers. Box05 output prime multiplication
decomposition count MAY include odd integers.
Below Box11, click button refuse
odd numbers. Box12 output not include odd integers.
201606301529 stop
<a name="docA051">
201606301743 start
After 20160623 upload
http://freeman2.com/prime_e1.htm
added the following boxes.
Box07
<a name="docA052"> 201606301748 here button add "2,2000" to Integer ends [example⇒] do not add long data to bigger [textarea] box. If click program output integer list to Box08 start from 2 end at 2000 build increase sequence. On the other hand Integer upper/lower bounds build increase and build decrease sequence. <a name="docA053"> 201606241009 (a506241009) Liu,Hsinhan added to prime_e1.htm to solve real number calculation problem. Input at Box07 output to Box08. This real number calculator has function compatible to prime_e1.htm Click program write next to Box07 [[ 160392960=2*2*2*2*2*2*2*2*3*3*3*3*5*7*13*17 103=47+53+3 102=89+13 2=2 ]] <a name="docA054"> Click Box08 output answer [[ 1603929602*2*2*2*2*2*2*2*3*3*3*3*5*7*13*17 0 10347533 0 1028913 0 22 0 ]] <a name="docA055"> Program change '=' to '' and change '+' to '' allow user verify first input line 160392960=2*2*2*2*2*2*2*2*3*3*3*3*5*7*13*17 both side are equal and confirm third input line 89+13 indeed sum to 102, because 1028913=0 <a name="docA056"> If input 102=89+13*1 '+' and '*' show up at same line, auto conversion stop work. Click program write code lines to Box07. Click Box08 output regular real calculator answer. <a name="docA057"> Click program output to Box09 [[ maxDif=34; maxID=217; Max gap occur at prime=1327,1361 1 <== difference of 2,3 2 <== difference of 3,5 2 <== difference of 5,7 4 <== difference of 7,11 2 <== difference of 11,13 4 <== difference of 13,17 etc. 2 4 6 2 6 4 2 ..... ]] <a name="docA058"> Before you run full range prime difference, you may need to know how many stored in primeArr[]. Click read Box09 first line. If fill two numbers in and click code output to Box09 prime difference in this limited range. Prime difference list help you understand the prime density and distribution condition. <a name="docA059"> output full range prime and middle integer between two primes. output full range middle integer between two primes. Liu,Hsinhan 劉鑫漢 201606301839 stop <a name="docA060"> 201606302117 start 201606302100 created button. Click [ex0] program fill javascript code to Box07. Click build square sequence in Box08. Box08 first line is 'oupStr;' delete 'oupStr;' copy only integers to Box01, Click button let primeArr[] store squares. <a name="docA061"> Use prime as building block, factorize integer to prime multiplication and factorize integer to prime summation all success. Use square as building block, factorize integer to square multiplication and factorize integer to square summation all fail. Because prime is dense and square is sparse. See Prime Counting Function Graph http://freeman2.com/tute0058.htm#primeCountDraw click [A1] http://freeman2.com/primcnt1.png 201606302127 stop <a name=a507070052> 201607070052 Acer1 computer mouse pointer disappear two minutes, computer don_hidon_lo noise 7 or 8 times. a507070052 <a name="docA062"> 201607130921 start update 20160713 prime_e1.htm added drawing capability. Drawing board 6 produced the graph uploaded to http://freeman2.com/gevn5000.jpg Goldbach even 5000 http://freeman2.com/gint2000.jpg Goldbach int. 2000 After upload gevn5000.jpg , Liu,Hsinhan continue improve drawing code and get Drawing board 1,2,3,4,5 20160711 LiuHH find 'improved' drawing board can not draw points greater than 500. But earlier file 07/08/2016 09:41 PM 551,166 prime_e1_v59_first_draw.htm can draw 2500 points ! What is the trouble? LiuHH included 20160708 drawing code to prime_e1.htm 07/11/2016 08:12 PM 661,734 prime_e1_v68_drawSum_v59().htm and name this older code as Drawing board 6 <a name="docA063"> Drawing board 6 has next control boxes/buttonsGraph Message ; Fill integer to Box31, click [sumSilent] click [draw Sum]
<a name="docA064"> 201607130951 here Drawing board 6 read input data from Box31. User can copy paste integers to Box31. Integers should be positive and increase order. Green box and button help you build input data. Left green box define integer begin, integer end and step size. In most case use 2,300 for faster draw. In "2,5001", 2 is first inrange integer. 5001 is first outrange integer. LiuHH's Acer1 computer draw "2,5001" continuous integer graph. But vary gap integer under 5000 fail. <a name="docA065"> Right green box has the following six choices 1:=integer [Fbounds] continuous integer 2 to 5000 2:=prime in [Fbounds] prime under 5000 3:=pr Middle [Fbounds] prime middle under 5000 4:=Pr+Middle [Fbounds] prime+middle under 5000 5:=even in [Fbounds] even number under 5000 6:=step in [Fbounds] step number under 5000 Prime 43 and prime 47 has middle (43+47)/2=45 prime middle list 2.5,4,6,9,12,15,18,21,26, ... prime+middle list 2,2.5,3,3,4,5,5,6,7,7,9,11... <a name="docA066"> If left green box has three numbers 2,5000,8 If right green box has 6:=step in [Fbounds] Click [BuildData to Box31] Box31 list 2,10,18,26,34,42,50,58,66,74,82,..... Green box and [BuildData to Box31] are utilities help user build simple data. Assume build Box31 data as next prime middle 4,6,9,12,15,18,21,26,30,34,39,42,45,50,56,60,64,69,72,76,81,86,93, <a name="docA067"> next click program produce [[ 4=2+2 6=3+3 9=3+3+3 <= integer 9, prime 3 has three count 12=7+5 15=7+5+3 18=13+5 18=11+7 21=13+5+3 21=11+7+3 26=23+3 26=19+7 26=13+13 30=23+7 30=19+11 30=17+13 34=31+3 34=29+5 34=23+11 34=17+17 39=31+5+3 39=29+7+3 39=23+13+3 39=19+17+3 ..... ]] <a name="docA068"> prime incremental summation is next 2,3,5,7,11 ..... [[      4: 2     6: 2,2    9: 2,5    <= to integer 9, prime sum to 5 count 12: 2,5,1,1  15: 2,6,2,2  18: 2,6,3,3,1,1 21: 2,8,4,4,2,2 26: 2,9,4,5,2,4,0,1,1 30: 2,9,4,6,3,5,1,2,2 34: 2,10,5,6,4,5,3,2,3,1,1 39: 2,14,6,7,4,6,4,3,4,2,2 42: 2,14,7,7,5,7,4,4,5,3,3,1 45: 2,18,8,7,6,8,4,5,6,4,4,2 ..... ]] <a name="docA069"> Click drawing code draw prime 3 curve (6,2) (9,5) (12,5) (15,6) ..... prime 5 curve (12,1) (15,2) (18,3) (21,4) ..... ..... Many think that prime show up randomly, but http://freeman2.com/gevn5000.jpg suggest that all prime same_jump at same_number_of_counts. gevn5000.jpg horizontal wave/wrinkle is a clue. 201607131052 here <a name="docA070"> Below Drawing board 6 , there is a message line Graph Message ; Fill integer to Box31, click [sumSilent] click [draw Sum] If click [sumSilent] message change to xaxis max. =498 , yaxis max. =25, second maxY=24. Adjust x/y min/max below 'x_y'. If click [draw Sum] message change to [draw Sum] Begin=20160713091945.192, End=20160713091956.717: 11.525 sec <a name="docA071"> Drawing board 6 need manual change x/y min/max If use then x maximum should be 5000 [sumSilent] message suggest x maximum and y maximum xaxis max. =1999 , yaxis max. =27060, second maxY=602. Adjust x/y min/max below 'x_y' If input has even only, yaxis max. and second maxY are the same. If input has odd number, yaxis max. is much greater than second maxY. Because all odd number has prime 3 39=31+5+3 39=29+7+3 39=23+13+3 39=19+17+3 <a name="docA072"> In odd=even+3 the yaxis max. =27060, second maxY=602. First maximum and second maximum have big difference. In this case follow second maxY=602, in y max:[ box ] fill 600. Ignore prime 3 first maximum=27060 . is a button work and created gevn5000.jpg [draw Sum] still fail draw prime middle < 5000 is a button attempt find out why program freeze forever. Not done yet. 201607131128 stop <a name="docA073"> 201607131530 start Above is Box31 and drawing board 6. Below is Box21 and drawing board 1,2,3,4,5. drawing board 1,2,3,4,5 CHANGEDRUN:☞ ; ; ; function drawSum( );
<a name="docA074"> 201607131538 here and initially are two separate buttons. Later [Draw yellow box] included [sumSilent] function. Now click [Draw yellow box] code read all yellow boxes and run [sumSilent] and draw at once. Ebounds specify input data begin, end and step values. Code build input data to Box31. If you have data in hand and not need code build data, in second box choose "7:=Box21 data as is" <a name="docA075"> Next data type box has next choices. 1:=integer [Ebounds] 2:=prime in [Ebounds] 3:=pr Middle [Ebounds] 4:=Pr+Middle [Ebounds] 5:=even in [Ebounds] 6:=step in [Ebounds] 7:=Box21 data as is Click box and choose one value. is one click for all button. If you do not want [Draw yellow box] build data, choose "7:=Box21 data as is" Compare with Box31 input RUN=☞ user must click to build data, green box do not have "7:=Box21 data as is" <a name="docA076"> Next yellow box attempt auto change drawing board 5 x/y min/max range. Free user from worry x/y scale. This is LiuHH's attempt, not work perfect now. Other choice is "Manual scale x,y" <a name="docA077"> Next yellow box choose one drawing from five possible boards. Four smaller board and one bigger board. Five board allow user put graph side by side compare. <a name="docA078"> Next yellow box choose output method. Choices are Graph, no VML VML, no Graph SLOW,Graph & VML <a name="docA079"> Next silver box When code is done, silver box will change to yellow box. Choices are Goldbach Prime sum 14=11+3 Prime multiplication 14=2*7 Log Prime multiplication <a name="docA080"> Today 201607131618 main work is integer's prime summation decomposition. integer's prime multiplication decomposition is future work. sum. decomp. all prime show up nearly equal. mul. decomp. prime 2,3 show up higher than other. For this consideration, "Log Prime multiplication" is a choice. "⇐ active" point to yellow boxes, compare with silver box, which is inactive. <a name="docA081"> change board five x/y min/max range such that it is possible zoom in gevn5000.jpg graph obstacles in greater detail. Not work now 201607131628. is debug button try find out why prime_middle has infinite loop and find out how to write zoom in code. <a name="docA082"> 20160711171540 reproduce gevn5000.jpg 20160711171620 get graph in 40 seconds Liu,Hsinhan's computer is Acer computer Aspire 5750Z4830. MSIE 9.0 Version:9.0.8112.16421 gevn5000.jpg draw even number under 5000. Total 5000/2=2500 points. Each time draw gevn5000 OK. Twice draw even number under 10000. Both time MSIE VML stop work after one minute. not freeze screen. <a name=a507151415> 201607151415 realize why "MSIE VML stop work after one minute" Because prime_e1.htm define prime up to 5000. When run 10000, LiuHH forget to define more prime numbers. 201607151421 redo "draw even number under 10000" save graph as http://freeman2.com/gev10000.jpg 07/15/2016 03:35 PM 439,850 gev10000.jpg 07/09/2016 05:42 AM 94,382 gevn5000.jpg 07/09/2016 11:10 AM 115,204 gint2000.jpg gevn5000.jpg and gint2000.jpg are compressed. gev10000.jpg keep bigger file size for better resolution. Because gev10000.jpg draw to 10000. 201607151550 record <a name="docA083"> Many times draw prime middle for prime less than 5000 There are 669 middle points. For example prime 19 and 23 has middle point (19+23)/2=21 Each time run prime middle always run one hour and freeze MSIE. See screen shot http://freeman2.com/priminf0.jpg User run this page has risk freeze your computer! 201607131646 stop <a name="docA084"> 201607151616 start Update 20160715 explain why "MSIE VML stop work after one minute" 201607151421 redo "draw even number under 10000" upload to http://freeman2.com/gev10000.jpg 201607142007 use YTD download https://www.youtube.com/watch?v=PtsrAw1LR3E https://www.youtube.com/watch?v=yPrbArbhPxk https://www.youtube.com/watch?v=pO7Egc5Dtqs <a name="docA085"> 201607150911 play Math Mornings at Yale_ The Patterns in the Primes, with Andrew Granville.mp4 1:00:14 201607151047 done 201607151049 play Terence Tao_ Structure and Randomness in the Prime Numbers, UCLA.mp4 47:50 201607151342 done 201607151344 play Introduction to Higher Mathematics  Lecture 10_ Number Theory.mp4 201607151839 done <a name="docA086"> 201607151415 realize why "MSIE VML stop work after one minute" 201607151421 build gev10000.jpg 201607151624 record 201607151652 upload gev10000.jpg <a name="docA087"> 201607192045 update 20160719 added Box41 input and output to Box42 Box43 Box44. Input is even integers 6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,... Output is Box42 output even Meet Prime, example 20: 3,7,13,17, Box43 output Prime Meet Even, example 991: 994,996,998 Box44 output Prime 012 list , example 967: 111011011010011 Liu,Hsinhan main goal is Prime 012 list. After create gint2000.jpg , gevn5000.jpg , and gev10000.jpg graph show horizontal stripe which is a puzzle. With in hand, horizontal stripe mystery solved, see http://freeman2.com/tute0067.htm#docA019 http://freeman2.com/tute0067.htm#docA043 http://freeman2.com/tute0067.htm#tute0067_index 201607192059 stop <a name="docA088"> 201607281533 start Update 20160728 improved code efficiency. Earlier version if input nonprime 33 to Odd number  odd prime= If primeArr[] stored million primes, program find 33 all the way to list end. But when search passed 37, future data always greater than 33. No need search future data. Similiar trouble exist in other place. Improved code stop search after prime is greater than integer. <a name="docA089"> Update 20160728 added above Box02, Box06, Box42. Define primeA6n[] but no output to save time. Added below Box09 output to Box09 and below Box47 output to Box47. <a name="docA090"> Update 20160728 added drawing board seven graph function. Click program fill data to Box41. Next click let program define summet array. To see the structure of summet goto prime_e1.htm Box48, click After click define summet, next click , wait for 10 seconds to 40 seconds to get graph like http://freeman2.com/gevmpri0.jpg //spend 10 seconds http://freeman2.com/gevmpri1.jpg //spend 35 seconds <a name="docA091"> Drawing board seven graph mark 6*n+1 type prime with red vertical bar, mark 6*n1 type prime with blue horizontal bar. If one even number meet ONLY red bar program draw a thin red vertical solid line over them. If one even number meet nearly all red bar except top most be a blue bar, program draw a thin red dot line over them. If one even number meet ONLY blue bar, program draw a thin blue solid line over them. Prime 3 cannot fit 6*n+1 or 6*n1 , program define 3 be red bar. Prime 5 is first prime fit 6*n1 , program draw prime 5 be blue bar. Thin red vertical solid line and thin blue solid line worth our attention. See more about gevmpri0.jpg and gevmpri1.jpg at http://freeman2.com/tute0067.htm#docA052 201607281610 stop <a name="docA092"> 201607282145 start Update a507282055 = Update 201607282055 201607282055 made code correction, allow program draw blue dot lines. Blue dot line mean on that line most prime are 6*n1 type only very top and very bottom are 6*n+1 type. Earlier version program can draw red dot line, but was unable to draw blue dot. Now identify blue dot lines help reader think prime structure. 201607282150 stop <a name="docA093"> 201608051633 start Update 20160806 added prime multiplication decomposition RUN%☞ Drawing board 1,2,3,4,5 has three color groups. Yellow Goldbach conjecture Red Goldbach conjecture Green prime multiplication decomposition Control arrangement is next.prime summation decomposition RUN:☞ ; drawSum_a50719_upload();
<a name="docA094">
201608051650 here
Button call drawSum_a50719_upload()
Button call drawSum()
Button call drawMul()
prime summation decomposition example 10=7+3, 10=5+5
prime multiplication decomposition 120=2^3 * 3^1 * 5^1
<a name="docA095">
Initially, drawSum() has one version.
201607082325 drawSum_v59() created gevn5000.jpg
Later version drawSum() cannot draw graph, trap in
infinite loop. 20160719 drawSum_a50719_upload()
has graph capability. Liu,Hsinhan continue correct
drawSum() but was unable to find why draw 2 to 5000
get graph, draw 2 to 300 get graph, draw 2 to 1000
can never get graph. This problem is not solved.
Final version drawSum() draw 2 to 1000 limit to
primeID=1 to 10 get graph for integer up to 1000.
primeArr[167]=997 There are 168 primes under 1000.
Program draw 10/168 reduce load and show 10 curves.
Look like rainbow, and mark "draw rainbow" If user
click number auto increase.
To decrease number, highlight and type number.
<a name="docA096">
Yellow read five yellow boxes, and do as
box show.
control input integer start end value.
Step value is used only if ask
select data type. Default [1:=integer]
To draw use data type [1:=integer]
To draw use data type [5:=even ]
If draw use data type [1:=integer ] each
odd contribute several prime3, and prime3 curve shoot
to sky immediately.
If draw red [DrawSum %%] read all yellow
box and read red box
<a name="docA097">
If draw green [DrawMul()] read all yellow
box and read red box and read
green box
If draw prime multiplication decomposition from 2 to
1000. Each even has one prime2. 64 has prime2 six
times then prime2 curve value is higher than other
prime curve. For example integer 2 to 1000
//[mulToBox] Integer prime mul, prime total count.
2: 994
3: 498
5: 249
7: 164
11: 98
13: 81
17: 61
.....
971: 1
977: 1
983: 1
991: 1
997: 1
<a name="docA098">
In this case if change green box from
'Prime multiplication 14=2*7'
to 'Log Prime multiplication'
Output curve is log scale and may look clearer.
Sample output
http://freeman2.com/pmul300a.jpg //Y axis is linear
http://freeman2.com/pmul300b.jpg //Y axis is log()
pmul300a.jpg 20160803215857.170 elapse=54.327 sec.
pmul300b.jpg 20160804013148.277 elapse=53.21 sec.
201608051755 stop
<a name="docA099">
201608051936 start
Below Box07 find ♫ , click program fill code
to Box07, click get output at
Box08. Prime ID range from 0,1,2,3,4,5 ... to what
ever defined. primeArr[pID] output prime number.
pID can be 0,2,4,6,8 even, for pID>0 primeArr[pID]
always be odd prime number.
Another file http://freeman2.com/prime_e2.htm#bx07
same button, also supply
primeA6n[pID] //0 if prime=6*n1; 1 if prime=6*n+1
primeGap[pID] //gap follow primeA; primeA+gap=primeB
prime_e1.htm start up with prime defined to 5003
prime_e2.htm start up with prime defined to 1000003
prime_e2.htm also define primeA6n[] and primeGap[]
201608051947
<a name="docA100">
201703281616
Update 20170329 add horizontal line in
even meet prime graph
Array primeArr[] store prime, use primeID (pID)
as index. First few are
pID : 0, 1, 2, 3, 4, 5, 6, 7, 8,...
prime : 2, 3, 5, 7, 11, 13, 17, 19, 23,...
primeArr[2]=5, primeArr[8]=23 etc.
In even meet prime graph y axis is primeID (pID).
Choose pID that is because save space in vertical
direction. On the other hand, if y axis draw prime
within same vertical space, graph contain less data.
y axis use pID it has disadvantage. If use y=prime
then consecutive 197, 199, 211 show gap in scale. If
use y=pID, prime 197, 199, 211 become pID 44,45,46
gap scale lost.
<a name="docA101">
201703242109 add
GapSeq
;
;
;
201703281645 here If fill [4,2] to above box, ask program mark gap sequence 4,2 Output will draw a purple horizontal line. Consecutive prime set 7, 11, 13 and 13, 17, 19 and 37, 41, 43 all have gap sequence 4,2. First primeID 3,5,11 has a purple horizontal line. pID 3=prime 7, pID 5=prime 13, pID 11=prime 37. This function compensate "gap scale lost" problem. 201703281657 <a name="docA102"> 201703282136 To draw http://freeman2.com/gevmpri1.jpg in even meet prime graph click buttons click the following set up graph x,y range create even numbers build graph data in prime_e1.htm draw gevmpri1.jpg User should get gevmpri1.jpg LiuHH drawing time is next [drawSummet] Begin=20170328214703.064, End=20170328214736.612: 33.548 sec When read gevmpri1.jpg , you may need next table http://freeman2.com/prim6n01.htm In prim6n01.htm 6*n1 prime are blue bars in gevmpri1.jpg In prim6n01.htm 6*n+1 prime are red bars in gevmpri1.jpg 201703282156[=][=]