Start up time program auto build long prime list from 2 to 5000011.
Build primeA6n[] list and build primeAgp[] . Wait about 20 sec.
Prime Both 18=13+5=11+7 and 18=2*3*3 a605131705
Even Meet Prime table Fast ; update 2017-05-30
Other prime web pages usage p[1]=2, p[2]=3, p[3]=5, p[4]=7 ... p[0]=2, p[1]=3, p[2]=5, p[3]=7 ...
because prime_e2.htm follow javascript index start from 0.
2016-08-29-07-29 record
prime_e4.htm index
program , Arndt , jsprime2.htm DocA , first upload 2016-08-06
XYGraph v2.3 - web page graph   ☜☞   donate   get code
Prime Counting Function Graph tute0058.htm#primeCountDraw click [A1]
Prime Counting >> Square Counting ; ∑(1/Sq.)=π*π/6 , ∑(1/prime)→∞
see proof at to docA454
The Cauchy-Schwarz Master Class   J. Michael Steele   ★★★★★
Please use MSIE browser to read this file.
Program environment Acer computer Aspire 5750Z-4830.
MSIE 9.0 Version:9.0.8112.16421
This file is personal home work. No one
proofread. Cannot promise correctness.
If you suspect any view point wrong,
please ask a math expert near by.
Freeman 2009-06-19-10-46

Liu,Hsinhan is not a professional programmer and
not a mathematics major graduate. This page may
contain error or low efficiency code.

Liu,Hsinhan 劉鑫漢 2016-08-12-19-18

Prime number calculator prime_e4.htm index
All document are in help click button or output top/bottom.

✚✚ Prime Gap Rules , Six n harmony rule = avoid_Prime3_cut rule
   Prime5 cut rule , include 7,11,13,17,19
✚✚ Consecutive Prime Gaps 20,14 allowed? or not allowed?
   input box and click button [Allowed?] , [prime5cut()]

✚✚ Bulk Harmony Rule checker allow gap sequence cross several lines.
    yellow input, BoxPGR output, [Allowed?] read one line gap sequence.
✚✚ Click RUN14 four buttons first, click RUN5 Build html table
   for prime gap mod(6)=0,2,4 and consecutive n count.
✚✚ [Build prime list] prime definition read user prime table
   define fake prime table see why squares cannot replace prime?

✚✚ output prime table, gap sequence, gap up/down sequence
   6*n+1 prime or 6*n-1 prime

✚✚ integer's prime multiplication factorization
   change 2200 to 2^3 * 5^2 * 11^1 or to 2*2*2*5*5*11
✚✚ set gap number, example gap=8, first pair is 89, 97
   list squeezed composite 90,91,92,93,94,95,96
✚✚ set gap number, example gap=8, first pair is 89, 97
   list squeezed middle 93,363,393,405,453,483,495,687, ...
✚✚ set gap number, example gap=12, first pair is 199,211
   list double prime pair 199,211; 211,223; 467,479; 509,521 ...
✚✚ set gap number, example gap=12, first pair is 199,211
   list double pair middle number 205,217,473,515,625 ...
✚✚ set gap number, example gap=8, first pair is 89, 97
   list squeezed composite + prime pair + outer two neighbor
✚✚ set Upper/Lower bound, output prime number and middle
   gap size is not considered. all prime in U/L bound listed

✚✚ gap sequence finder, input gap sequence 6,6,2 output all match primes
gap up/down finder, gap always >=2, gap up/down can be positive or negative

✚✚ [prime difference] that is prime gap. list in Box12
   [gap difference] that is gap up/down list. same list also in Box02
✚✚ Goldbach conjecture. integer's prime summation factorization change
   22 to 11+11=17+5=19+3 Box14 random input, U/L bounds sequence input

Goldbach conjecture all even>=6 = primeA+primeB
6n-1 type prime short as 0, 6n+1 as 1, prime 3 mark 3.
Even 42 has 4 6n+1 type, total 8 primes, other 4 be 6n-1
List those primes not enter Goldbach even decomposition
List Goldbach dropped primes in consecutive pieces
Each even list all primes and mark Goldbach_ok or no
given begin even,prime and end even, code find end prime
User set begin even, end even at U/L bounds set begin prime at green
box right to "Pave road auto " above example use prime 89 for begin (x,y)=(206,89)
Pave road auto ask user input even and prime; Pave road force ask user input nID,pID. and gevmpri1.jpg use only nID and pID.
Pave road auto answer not match gevmpri1.jpg end pID ; Pave Road Force ask user guide.
Above all goto Box14 under Box14 click green one line box to select.
and goto Box15 below Box15 click [Pave Road Force]
All document are in help click button or output top/bottom. 2016-10-08-10-08 here
✚✚ prime gap summary within primeArr[] defined range, gap=2 has 32463 count
   gap=4 has 32307 count ... gap=116, no match found ; gap=154, has 1 count
✚✚ Display Box17 primes are 6*n+1 prime or 6*n-1 prime. Output to Box18
   example [exV] , click [prime6n±1] Box18 output. See [prime6n±1 help]
✚✚ [6*n+1-1] integer Bgn/End, 6*n is integer. 6*n±1 is prime , If n has both 6*n±1
be prime, mark A. only 6*n+1=prime, mark B. only 6*n-1=prime, mark C. No prime D.

✚✚ Fast Even Meet Prime table builder
   Use given prime list and manipulate index to build table
✚✚ primeBoth list builder
   Calculate 18=13+5=11+7 and 18=2*3*3
✚✚ sin(), cos(), exp() regular calculator. real number only, no complex. Auto change
   from 102=89+13 to 102-89-13 and evaluate to 0. Confirm 102=89+13 is OK.

<a name="program0">
Prime number calculator

Prime Gap Rules six n harmony rule visualization
Six n harmony rule = avoid_Prime3_cut rule.
6*n-1 prime cross n line, 6*n+1 prime cross n line in turn.
Prime has 6*n-1 and 6*n+1 two groups. Consecutive prime difference is prime gap.
Let p(k+1)-p(k)=g(k) Except prime 2 and 3, prime gap is always even number.
primeGap%6 has 0, 2, 4 three possible values.
primeGap%6=0 say p(k+1) and p(k) both be 6*n-1 or both be 6*n+1.
primeGap%6=2 say p(k) is 6*n-1 and p(k+1) is 6*n+1 . Example 17+2=19
17=6*3-1 , 19=6*3+1 . Gap 2,8,14,20 etc. must be from 6*n-1 to 6*n+1
primeGap%6=4 say p(k) is 6*n+1 and p(k+1) is 6*m-1 . Example 19+4=23
19=6*3+1 , 23=6*4-1 . Gap 4,10,16,22 etc. must be from 6*n+1 to 6*m-1
primeGap%6=2 gap follow primeGap%6=2 is forbidden.
primeGap%6=4 gap follow primeGap%6=4 is forbidden.
primeGap%6=2 gap follow primeGap%6=4 is allowed.
primeGap%6=4 gap follow primeGap%6=2 is allowed.
Gap 2,2 is not allowed, ONLY initial prime 3,5,7 has gap sequence 2,2 .
Gap 20,12,14 is not allowed, 12%6=0 is transparent, 20%6=2,14%6=2 forbidden.
Prime5 cut rule , include 7,11,13,17,19
Allowed gap sequence may be cut off by composite contain 5,7 etc.
Gap sequence 6,6,6,6 void by multiple of five, 6,6,6,6 never show up.
Gap 6,4,2,4,2,4 void by multiple of seven. 6,4,2,4,2,4 never show up.
Input your prime sequence in yellow box below.
Click [Allowed?] to test Six n harmony rule.
Click [prime5cut()] to test Prime5 cut rule.
Liu,Hsinhan 劉鑫漢 2016-08-16-23-25
p(k) is k-th prime. k in p(k) and n in 6*n-1 are independent. a508170626 "p p+2 p+6 p+8 : A007530" is 2,4,2 in prime_e2.htm a508241428
Six n harmony rule is in fact avoid_Prime3_cut rule. 2016-08-24-16-02

<a name="bxPGR"> 2016-08-17-10-16 in prime_e2.htm use BoxPGR
Consecutive Prime Gaps 10,10 allowed? or not allowed? Please input and test.
Next yellow box INPUT Prime Consecutive Gaps , click Example buttons.
Example ,,,, ; ,,,, ; [,,,] six n harmony rule
yellow input, BoxPGR output        
Above six n harmony rule exam, below prime 5,7,11 cut exam are independent.
prime 5,7,11 cut RUN ☞ yellow box, blue box input, BoxPGR output
exam prime from prime 5 to prime expect a small prime for [prime5cut()]

yellowbox example , , , , ;  prime 5 to prime  
RUN ☞ yellow and pink box input, BoxPGR output
output long or short ? output short few 1
PGR=Prime Gap Rules ; QEboxcPGR.value='' ;

modsix024, short024, group024, ascend024 main goal is direction study. Prime has 6*n-1
and 6*n+1 two groups. Gap%6=2 must be from 6*n-1 to 6*n+1. Gap%6=4 must be
from 6*n+1 to 6*n-1. Gap%6=0 must be from 6*n-1 to 6*n-1 or from 6*n+1 to 6*n+1.
primeArr[] is 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71 ...
primeAgp[] is 1,2,2,4,2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4 ...
modsix024[]=gap%6 . Mod(6) remainder has 0,2,4 three values. 0,2,4 are direction.
short024 change from modsix024[]=2,4,2,4,2,4,0,2,0,4,2,4,0,0,2,0,4,2,0,4, ...
to short024[]=26,01,21,01,43,02,21,01,42,01,41,01,28,01,23,02,41,02, ...
group024 change short024 to 0 group, 2 group, 4 group. (0,2,4 are direction)
ascend024 arrange 0 group, 2 group, 4 group in ascending order.
list024 read user input and list direction 0,2,4 to output box. Help user study.
2016-09-19-18-41 start, 2016-09-19-19-20 stop

six n harmony rule visualization. Ignore initial prime 2,3; ignore initial prime gap 1,2. All
gap%6=0 are transparent, gap sequence must be 2,4 in turn. Click [modsix024] see BoxPGA.
gap sequence direction data, output only 0,2,4 RUN ☞
BoxPGA   Yellow is one series calculation, green is another

QEboxcPGA.value='' ; Long prime gap sequence example or input your gap sequence
BoxPGA input RUN ☞ BoxPGB output

<a name="bxPGB"> click [modsix024 ], build modsix024[] array first.
Compact [modsix024] data, input from modsix024[] RUN ☞ output to BoxPGB
BoxPGB   short 26,01; drop pID ;


<a name="bxPGC"> ; click [short024 ], build short024[] array first.
Separate [short024] data to 0,2,4 groups, RUN ☞ id=QEspangroup024
BoxPGC   ;

Click RUN14 four buttons, then click RUN5 [list024] to build Primegap Modsix Short Table
QEspanPrimeCount.innerHTML='' ;
Click one by one RUN14 ☞ , , ,
QEspanascend024.innerHTML='' ;
list024 example RUN5 ☞ output to BoxPGD ; index
Prime gap modsix begin/end

BoxPGD   ; ask list024


Build prime table
Box01:prime table; Box02:input integer; Box03:output factorized integer;
Box04:input integer factorization list, click [Prime counting] Box05:output summary
Box01   ; paste user prime list to Box01 or prime list

Build⇒ up to ,
in Box02 Show primeID , prime , gap , gap%6 , gapUp/Down , 6*n±1
Box02 data column ↕ to ↔ row change , RUN ☞
upper_lower bounds , default number 1 to 5001
Box02   ;

QAboxc02.value='' ; already merge to [Build prime list]

integer's prime factorization. 2200=2^3 * 5^2 * 11^1
[factorize integer pow] and [factorize integer mul] read input from Box03, output to Box04.
Work is integer's prime factorization. For example, [factorize integer pow] change from
composite 2200 to prime multiplication 2^3 * 5^2 * 11^1 . Button [factorize integer mul]
output to 2200=2*2*2*5*5*11 . Button [integer list] help you build continuous integers.
Box03   ; Integer ends output to Box03

example: , , , RUN ☞ ,
Box04 ; [factorize integer] Box03 input, Box04 output ; index

Box04 in Box05 out
Box05   QAboxc05.value=''


Assume Prime Upper/Lower bound has [2,2000], assume One prime gap has [8]
Click [squeezed number] output [2,2000] all prime gap=8 in-gap composite numbers.
Default input has first gap output 90,91,92,93,94,95,96 seven composite. Purpose
is to study squeezed composite their prime multiplication factorization has what
special point relate to 8 (gap size). a508181641
U/L bound box use comma [2,2000] mean 2 and 2000 are both integers.
U/L bound box use column [2:2000] mean 2 and 2000 are both primeID.
Initial primes are 2,3,5,7,11,13,17,19 ... ; primeID=pID=0,1,2,3,4,5,6,7 ...
This page use pID=0 for first prime 2. Some other page use pID=1 for prime 2.
prime pair squeezed integers, middle integer
Prime Upper/Lower bound06 One prime gap
Box06 ; yellow box input output to box06

Second [squeezed number] , near [squeezed middle] ;
[squeezed middle] input is box06, output to box07. If assign [8] to One prime gap box.
Click [squeezed number], box06 has squeezed composite numbers 90,91,92,93,94,95,96 .
MUST be odd count squeezed numbers. Click [squeezed middle] output to box07 93, 363,
393, 405, 453, 483, 495, ... They are all squeezed middle number. Program copy first
squeezed gap ALL numbers for reference. Start from second gap, copy only middle ONE
number. Purpose find whether squeezed middle has special point.
Click in output choice green box, allow you change middle to other choice.
Output choice ,
Box07 [squeezed middle] alert here

QBboxc07.value='' ;

prime pair listed for given gap
[Double prime] read Upper/Lower bound and read prime gap value. Assume prime gap=12.
Output to Box08 all gap=12 prime to Box08. One line two primes. Each line prime pair
all have difference=12. Purpose is to identify gap=12 prime pairs within Upper/Lower bound.
Prime Upper/Lower bound08 One prime gap
Box08 ; yellow box input output to box08

Input from [Prime Upper/Lower bound08] and [One prime gap]
Output squeezed composite middle number. and output OUTSIDE-gap MIDDLE number.
Assume prime gap=12, prime pairs 199,211 and 211,223 and 467,479 all be gap=12 .
199,211 has middle=205 ; 211,223 has middle=217 ; 467,479 has middle=473 .
From 223 to 467 it has middle=345 . Box09 output in-gap middles 205,217,473
also record OUT-gap middles 211,345,494 etc. Purpose is to see if middle points
contain any secret? 2016-08-19-21-21 record


prime pair + squeezed
[squeezed+prime] list [squeezed number] and its primes.
Assume Prime Upper/Lower bound10 box has [2,2000] , assume One prime gap box has 8.
click [squeezed+prime] Box10 output gap8 prime pair within 2,2000 . First gap8 prime pair
is 89,97 (97=89+8) Box10 output first section 88,89,90,91,92,93,94,95,96,97,98
This section include gap8 prime pair 89,97 those squeezed number 90,91,92,93,94,95,96
and outside number 88,98 . Purpose is to study whether squeezed+prime section has
common characters. For example, analysis [88,89,90,91,92,93,94,95,96,97,98] using
integer's prime multiplication factorization and integer's prime summation factorization

Prime Upper/Lower bound10 One prime gap
Box10 ; output to Box10 ; defined prime

[prime+middle] read Middle Upper/Lower bound10 box numbers 2,2000 (example).
output prime number and middle point of two neighbor primes within 2,2000 .
[middle] button output middle point only. Purpose is to study middle point.
[prime+middle] button and [middle] button output to box10.
Middle Upper/Lower bound10
; ; box goto 03 ;

gap sequence finder , up/down finder ; index
Find gap sequence and match prime last digit? go here
Box11 allow user input specific gap sequence and search in defined prime list.
Box12 allow user input two integers and list prime gap sequence in range.
prime 5,7,11,13 say p=5 and 5,7,11,13 is "p p+2 p+6 p+8 : A007530"
prime 5,7,11,13 prime_e2 say gap is 2,4,2 that is "7-5, 11-7, 13-11"
If reader apply data to prime_e2.htm pay attention to the difference.
Each line prime add one 6n±1 ? line end not add 6*n±1
Example admissible:,,,, ; never: ,,,, ; [,,,]
gap sequence
Box11 ; ; defined prime

upper/lower bounds , default 1 to 5001
Example: ,,,,,,, ; ;
Box11 allow user input gap up/down sequence and search in defined prime list.
Box12 allow user input two integers and list gap up/down sequence in range.
gap = two consecutive prime difference. Greater - smaller prime, gap always >=0.
gap up/down = two consecutive gap difference. gap up/down can be >,=,< 0.
2016-08-23-11-10 cannon shock

QCboxc11.value='' ;

list prime gap = list prime difference
Prime list similar to distance, prime difference=gap similar to velocity,
gap difference similar to acceleration. Gap up/down variation is a topic.

Given two integers then click
program list prime gap, output to Box12. Click to see more data.
List all prime gaps output to Box12
Box12 ; Full range? How many primes defined ?

Given two integers then click
program list prime gap, output to Box12. Click to see more data.
List all gap differences output to Box12
Prime list similar to distance, prime difference=gap similar to velocity,
gap difference similar to acceleration. Gap up/down variation is a topic.

QCboxc12.value='' ;

2016-09-05-12-50 guess gap sequence 2,4,2,4 has finite count.
Because prime become far away gradually.
How to proof gap sequence 2,4,2,4 has finite count?
How to find gap sequence 2,4,2,4 total count?
One method is to study gap sequence 2,4,2,4 prime set dilute rate

Search gap sequence and match prime LAST digit.
[gapSeq & primEnd] help. Input format is [2,4,2 ; 1,3,7]
2,4,2 are gap sequence, semicolumn flag prime end digit begin.
1,3,7 are prime end digit. Example prime 11, 13, 17, 19 has
gap 2,4,2 and prime end digit 1,3,7. Purpose is to study why
gap sequence [2,4,2,4] must begin with prime end digit 1. If
gap sequence [2,4,2] and begin prime end digit 1 what number
void last prime? 2016-09-05-17-26 ; example ; ;
gap sequence ; prime last digit
green box input Box13 output
Box13 Integer output ; Box13 data column ↕ and ↔ row ,

upper.lower bounds , default number 1 to 5001
Box13 show jump set first prime pID , prime , 1/prime , jump , jump/prime
Above green box input Box13 output
[gapSeq diluteRate] help. Box13 default value jump/prime. Checkbox change default.
What is jump? If green box has [2,4,2,4 ; 1,3,7], click [gapSeq & primEnd], Box13 output
"11, 13, 17, 19, 23"; "101, 103, 107, 109, 113"; "1481, 1483, 1487, 1489, 1493"; etc.
First jump: 101-11=90, second jump: 1481-101=1380, third jump: 16061-1481=14580
Gap sequence "2,4,2,4" show up rare and rare (dilute rate). Guess (no proof) gap
sequence "2,4,2,4" has finite count. Because future gap become larger and larger.
Small size "2,4,2,4" cannot persist (guess, need proof). 2016-09-06-10-38
QDboxc13.value='' ;

Goldbach conjecture
Box03 integer's prime multiplication factorization 22=2*11 ;
Box14 integer's prime summation factorization 22=11+11=17+5=19+3
German mathematician C. Goldbach (1690~1764) in his letter addressed
to Swiss mathematician L. Euler (1707~1783), Goldbach wrote:
Proposition (A) Every even integer ( ≥ 6 ) is the sum of two odd primes;
Proposition (B) Every odd integer ( ≥ 9 ) is the sum of three odd primes.
They were called Goldbach conjecture.
2016-06-19-09-47 Liu,Hsinhan access and 2016-06-25-15-55 copied

Prime SUMMATION factorization random integer input to Box14 , output to Box15.
Box15 output even=primeA+primeB, if find 16=7+9, 9 is not a prime, Box15 not list.
If next Odd subtract box number end with ';', Box15 output "no match primes+0"
Odd number - odd prime= white box number end with ';' or not?
Integer to prime summation. Click [prime sum random] input Box14, output Box15.
or Click [prime sum seq.] input Integer upper/lower bounds silver box, output Box15.
Box14 Prime sum random input ; , Goldbach conjecture input

Two RUN buttons both do integer's prime summation factorization change 22 to 11+11=17+5=19+3
U/L bounds Silver box number end with ';' or not?
RUN ☞ read random integer from Box14, output to Box15.
RUN ☞   read silver box sequential input, output to Box15.
6*n±1 ? [Whitelane] output primeID
Green box decide what to do, click box to choose. checkbox for output pID or prime
Box15 Prime sum output [Detail], [Pave] debug? debug slow down.

RUN ☞ Next blue box input, Box15 output. index
Pave road force ,
Box14 or U/L bounds silver box input Box15 & 16 output
box goto 81 click [real number calculator] output to Box82. ,
Box16 debug How many primes defined ? ;

Example 370:241,251 370-241=129 or 370-251=119 a prime? composite?
[showComposite] input Box16, output Box16.
Box15 line "6=3+3" to Box81, [real number calculator] change to 6-3-3 answer 0 , mean OK.
QDboxc16.value=''; If U/L bounds silver box right end has ';', Box14 output even numbers only. is a Goldbach conjecture integer's prime summation factorization
graph. gevmpri0.jpg data can be compared with Box15 Prime sum output data. In U/L bounds [2,200]
enter 2,200. In 6*n±1 ? choose [24=11+5 6n-1,6m-1 ] then click [prime sum seq.] Output to Box15.
In 6*n±1 ? choose [42: 4/8 //4 6n+1, 8-4 6n-1 EVEN only] click [prime sum seq.] 2016-09-28-16-26

prime gap size and gap count
This file use primeArr[] to define prime list and use primeAgp[] to define prime gaps.
gap(n)=prime(n+1)-prime(n). Within primeArr[] definition, there are how many size=2
gaps? how many size=4 gaps? ... What size gap not present? Click [gapSum] ,
output to Box17. Some gap sequence never show up, for example 2,8 is forbidden.
Click [gapHelp] read Box17. Read Prime Gap Rules find out why 2,8 is forbidden.
Please visit Six n Prime Table from n=1 to 40000
This table give you evidence and convince you gap 2,8 is forbidden. a508232228

[gapSum] input is primeArr[] . Box01 click button [Build prime list] control.
[gapSum] button output to Box17 below. ,
Box17 output ; QDboxc17.value='' ;

<a name=a509130002>
Display Box17 primes are 6*n+1 prime or
6*n-1 prime. Output to Box18.

example , Box17 input Box18 output

6*n±1 each n neighbor one or two prime A,B,C,D list
Integer Bgn/End ;
Box18 output ; detail Y/N? No detail to Box18, faster.

BPrime is 6*n+1 type prime, CPrime is 6*n-1 type prime.
gap[n]=prime[n+1]-prime[n], gap=2,3,6,8,10 ... ; gap%6=0,2,4 Ratio
B:C sample , ; 0:2:4 sample ,
QDboxc18.value='' ;

Fast Even Meet Prime table builder. Use given prime list and
manipulate index to build table. Click [fast 3000], [empTblFast()], [show Box23 sum],
[go see table] Pay attention to table bottom elapse seconds. ,
Box21 input ;Ex.,,,, ,, , ,

U/L bound3 Silver box number end with ';' or not?
Given max. prime RUN 11 ☞ Box23 output htmlTableCode
Box22 output ; DRAW 12 ☞ , go see table

, , ,
Box23 output ; x 1,2 , y 3to9 ; , ;

QDboxc23.value='' ;

primeBoth list builder.
Input integer to Box31 (or click example button), enter Given max. prime to blue box.
Click RUN 31 ☞[primeBoth()] Next select prA,prB ; prA,odB ; odA,odB
Click [Goldbach favor/dislike] output to Box34,35,36,37. Click [gbk?] see help at Box38.
Box31 input ; Ex.,,,, ,, , ,

U/L bound3 Silver box number end with ';' or not?
Given max. prime RUN 31 ☞
Box32 output
Box33 ev=prA,prB,prC ;
x 1,2 , y 3to9 ; , , ; [*?] help button send to Box38
output prA,prB ; prA,odB ; odA,odB ; , ,
Box34 even=prA+prB ;
Box35 even=prA+odB ;
Box36 even=odA+odB ;
Box37 220=2*2*5*11
Box38 help ;
Box39 debug ; ,
DRAW 23 ☞ ,  noteA  
; QDboxc39.value='';

Real number calculator ; ; index
Box81 click ex0,ex1,ex2,♫pID then click [real number calculator]

Box81 input Box82 output , , , ,,
Box82 ; ; , ,

Integer ends= ; ,
Box83 ;

QPboxc82.value='' ;

<a name="docA001">
2017-05-20 upload 
prime_e4.htm has two points different from 
earlier version prime_e3.htm 
1. prime_e4.htm has fast code to find 
   Even Meet Prime table. See 
2. prime_e4.htm is a "Prime Both" page. 
   Both mean 18=13+5=11+7 and 18=2*3*3 
   Later Liu,Hsinhan will add 18=2*3*3 
   factor sum to Even Meet Prime table
   then become Prime Both Table.

<a name="docA002">
In prime_e3.htm Click [slow 3000], [evenMeetPrim0()], 
[empBorder()], [slow Box26 sum] Pay 
attention to table bottom elapse seconds.
Fast/Slow = 6/100 = 1.212/20.27 

Slow table whole table be given or future.
Fast table allow half table given (blue) 
and other half be future (yellow).

In Given max. prime enter a prime which is 
half way the value of input in Box21. 
Those integer <= Given max. prime are given.
Those integer >  Given max. prime are future.
[Given max. prime] must be >=101

<a name="docA003"> 
Goldbach conjecture say 
Every even integer ( ≥6 ) is the sum of two odd primes.
Goldbach like example     24=5+19=7+17=11+13
Goldbach leftover example 24=3+21 //only 3 is prime 
Goldbach dis-like example 24=9+15 //both are not prime.
Code send 5,19 , 7,17 , 11,13 to Box34.
Code send 3,21 to Box35.
Code send 9,15 to Box36.
Code send 24=2*2*2*3 to Box37.
Box34 to Box37 have detail data. 
Even Meet Prime table and primeBoth table sum 
above data to one number and list in table. 
Summation action change 5+19 + 7+17 + 11+13 
to 72. 

<a name="docA004">
In prime_e4.htm deleted slow Even meet Prime table 
user can goto prime_e3.htm#evenMeetPr find slow 
section. prime_e4.htm keep fast Even meet Prime 
In prime_e4.htm deleted PrimeBoth table. Box32 
has PrimeBoth table data. Liu,Hsinhan think that 
Box34 even=primeA+primeB
Box35 even=primeA+oddB 
Box36 even=oddA+oddB
detail data is much better than Box32 output 
Box32 add all primeA1+primeB1 + primeA2+primeB2
the lumped sum blurred detail data. User may 
pay attention to detail data, instead of lumped 

<a name="docA005">
2016-08-15 build Six n Prime Table 
from n=1
to n=400000
2016-08-16-23-25 Prime Gap Six n harmony rule 
stand out quickly. On the other hand,  
2016-07-27 build Even Meet Prime graph 
2017-04-16 build future data in hand
Until now 2017-05-30-10-19 Liu,Hsinhan do not 
have luck like Prime Gap Six n harmony rule. 
Even Meet Prime graph reveal anything useful? 
Liu,Hsinhan is still thinking. 


<a name=JavascriptIndex>
Javascript index   local
Save graph code to same folder as htm files.   local

Older Prime number and prime decomposition
jsprime2.htm first upload 2009-09-15

Goldbach conjecture data 6 to 1000

Prime number study notes

Six n Prime Table from n=1 to n=40000
ten table files .....
Six n Prime Table from n=360001 to n=400000

Prime number and prime decomposition (drawing board)
Chinese version 素數函數及整數之素數分解
prime_e1.htm first upload 2016-06-23

Prime number calculator 4
prime_e2.htm first upload 2016-08-06
prime_e3.htm first upload 2017-04-08
prime_e4.htm first upload 2017-05-20

Thank you for visiting Freeman's page. 
Freeman Liu,Hsinhan 劉鑫漢 2017-05-19-22-23

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