Start up time program auto build long prime list from 2 to 5000011.
Build primeA6n[] list and build primeGap[] . Wait about 20 sec.
Even meet Prime table a604011006 update 2017-08-04
Goldbach conjecture. integer to prime summation ; gevmpri0
Other prime web pages usage p=2, p=3, p=5, p=7 ...
freeman2.com/prime_e2.htm p=2, p=3, p=5, p=7 ...
because prime_e2.htm follow javascript index start from 0.
2016-08-29-07-29 record
prime_e3.htm index
program , Arndt , jsprime2.htm DocA
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 http://freeman2.com/tute0058.htm#docA403 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
contain error or low efficiency code.

Liu,Hsinhan　劉鑫漢　2016-08-12-19-18

Prime number calculator prime_e3.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
See http://freeman2.com/tute0068.htm#docA003
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.
http://freeman2.com/gevmpri0.jpg 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.
✚✚　Even meet Prime table
This is html table code graph. prime_e3.htm main topic.

✚✚　Future prime column sum list table builder
All given prime column sum list table builder
✚✚　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
oeis.org "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()]
BoxPGR

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 ...
primeGap[] 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 ☞
see
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 ;

QEboxcPGB.value=''

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

QEboxcPGC.value=''
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

QEboxcPGD.value='';
,

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 
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  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
Box09

QBboxc09.value=''

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 ;
QCboxc10.value='';

>

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 oeis.org 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 oeis.org 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
gap_up/down
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
https://arxiv.org/ftp/math/papers/0309/0309103.pdf

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.
index
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.
http://freeman2.com/gevmpri0.jpg 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 primeGap[] 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 http://freeman2.com/prim6n01.htm 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='' ;

How to color [table] [td] cell? //a604021537
 Prime gap table 2017-04-02-15-37 Prime gap table 2017-04-02-18-00
 a=outside b=6n-1 c=6n+1 d=prime3 e=unused 2017-04-03-06-02

Even meet Prime table click [RUN 11 ☞] , [DRAW 12 ☞]
In gevmpri0.jpg each primeID row shift to left end, same as primeID=1=prime3 row.
Even meet Prime table http://freeman2.com/emphtme1.jpg ; Box21 ,
Box21 input ; help , , , , , ,

Even meet Prime table click [gevmpr00()], below, [show Box22 table]
x axis is numberID, nID*2+6=even, nID start from 0 (number=6) , ,
y axis is primeID, primeArr[pID=0]=prime2; pID=1,prime3; pID=2,prime5; etc.
 Even 6 to x axis nID=0 to 97 cell fill table direction pID rowAlign keep (8)23 prime 2 to y axis pID=0 to 45 Horizontal normal yes
gevmpri0.jpg text table version RUN 11 ☞ next click [show Box22 table] below.
Box22 output ; RUN ⇒

QDboxc23.value='' ; <td class=b> replace , , , , ,
Box23 ; replace 13 ☞ , , , ; delList help

DRAW 12 ☞ , ; add ,,, ;

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.
Liu,Hsinhan 2017-04-10-22-00

Future prime column sum list table builder
Box24 output ; click [RUN 21 ⇒] , [RUN 22 ⇒] , [DRAW 23 ☞]

INPUT bgn , end RUN 21 ⇒
Ex. , , , , , ; RUN 22 ☞
Box25 output ; Help , ; unknown future column sum

Box26 table ; x 1,2 , y 3to9 ; , ;

DRAW 23 ☞ , ; ; ; QDboxc26.value=''

t068tbl8()


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

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

Integer ends= ; ,
QPboxc82.value='' ;
[=][=]

<a name="docA001"> update 2017-04-11
pr3index()
2017-04-11-14-00 start
This file http://freeman2.com/prime_e3.htm
first upload on 2017-04-08-21-36
Update 2017-04-11 in parameter control section

 Even 6 to x axis nID=0 to 97 cell fill table direction pID rowAlign keep (8)23 prime 2 to y axis pID=0 to 45 Horizontal normal yes
added right side two choices.
keep all  or other choice
and
(8)23 yes  or not.
If click [ all ] box, program change to [prime]
then change to [b:6n-1] to [c:6n+1] to [delPrim]
If choose keep prime  graph output only prime column.

<a name="docA002">
What is "prime column" ? In next graph

______prime13
______prime11
__#$__prime07 ______prime05 ___$__prime03
030507091113primGap
______x-axis

Bottom prime03 black/yellow row, a black square
indicate that column top start a new prime.
03,05,07,11,13 black squares all start a new
prime, but 09 yellow square '$' NOT start a new prime. From yellow square '$' move up to
top find red square '$' This red square '$' is
not prime07 row left most (first) red or blue.
(Red square '#' start a new prime07 row)
keep prime choice allow reader study the graph
pattern.

<a name="docA003">
All prime column has black prime3 at bottom. Column
top color reveal this red prime 6*n+1 (7,13,19 etc.)
or blue 6*n-1 (5,11,17 etc.) property. All color in
between are opposite to top color! An interesting
observation.
All non-prime column has yellow at column bottom and
mixed red/blue or all blue or all red. Worth further
study.

<a name="docA004">
(8)23 yes or not allow reader add extra
information to graph or delete it.
First upload, Box22 output no style definition,
if reader copy paste to other web page, table
has no color!. Update 2017-04-11 include
<style> definition to output box Box22.
2017-04-11-15-08

<a name="docA005"> update 2017-04-13
2017-04-13-10-48 start
update 2017-04-13 add click buttons in
http://freeman2.com/prime_e3.htm
DRAW ☞ ,;add ,,,
http://freeman2.com/emphtme1.jpg
under red, yellow, blue graph
106,04,13,11,00 cannon shock
there is a white row for x-axis. Main program
do not add number to x-axis white row, allow
narrow color bricks like emphtme1.jpg show.
When LiuHH write
http://freeman2.com/tute0068.htm
hand work insert numbers to x-axis white row.
If reader use table code in Box22 and also
insert numbers, then it is better write code
to do this job.

<a name="docA006">
pr3index()
In
http://freeman2.com/prime_e3.htm#evenMeetPr
click [gevmpr00()] create html table code in Box22.
click [show Box22 table] in prime_e3.htm display
html table. Above two clicks x-axis white row do
not have numbers. On the other hand,
click [gevmpr00()] create html table code in Box22.
click add [even] insert numbers to x-axis white row.
click [show Box22 table] display html table.
Above three clicks output even 06 08 10... in x-axis
white row, color bricks become wider.
click add [odd] insert odd 03 05 07 09 11...
click add [eo] insert even and odd.
click add [oe] insert odd and even.
User is free to adjust table appearance.
2017-04-13-11-23 stop

<a name="docA007">
2017-04-24-16-07
update 2017-05-03 added [ID2Prime] to control section

RUN ⇒
Click [EVmeetPR()] output nID and pID to Box22.
Click [ID2Prime] code change from nID, pID to
even and primes. That is change
from  9 , 2,3,4,5,6,7
to   24:5,7,11,13,17,19
Graph x-axis, y-axis use nID, pID .
human brain thinking need even and primes.
[EVmeetPR()] input at  output to Box22.
[ID2Prime] input at Box22, output to Box22.
2017-04-24-16-22

<a name="docA008">
2017-04-30-17-07

unknown future column sum
If let box be unchecked, output is same as
before. Code consider future as unknown see
Even Meet Prime Table 08, fog-red, fog-blue
boxes become fewer and fewer when move to right.

<a name="docA009">
ALL GIVEN column sum list
If let box be CHECKED, output is different. Code
consider all data be known. User can compare
two outputs and find unknown future column sum
error. Columns [6*n-1 drop] [6*n+1 drop]
[bluPrAll] [redPrAll] [bluPrSum] [redPrSum]
all work with 6*n-1 or 6*n+1 type primes.
Start from 5 to infinity. These columns sum
not include prime 3. Because 3 not fit 6*n±1.
But red/silver/pink [column sum] has prime 3.

<a name="docA010">
If you choose [ALL GIVEN column sum list],
prime bgn 31 , end 71 ;  click [RUN 21 ⇒] ,
[RUN 22 ⇒] , [DRAW 23 ☞] output has one row
prime 37 40 120 ... 80 37
bluPrSum=80 , redPrSum=37
blue + red = 80+37 =117, short 3 from 120
Prime3 enter [column sum] and not enter 6*n±1
calculation which cause difference.
2017-04-30-17-37

<a name="docA011">
pr3index()
2017-05-03-07-11

x 1,2 , y 3to9 ; , ;
Allow user extract two columns as (x,y) pair data and
use (x,y) to draw curve.
x selection is 1 or 2. In Future prime column sum list
column 1 is [odd number], column 2 is [even number] .
y selection is 3 or 4 or 5 or 6 or 7 or 8 or 9. In
Future prime column sum list
column 3 is [column sum], column 4 is [6*n-1 drop] ,
column 5 is [6*n+1 drop], column 6 is [ bluPrAll ] ,
column 7 is [ redPrAll ], column 8 is [ bluPrSum ] ,
column 9 is [ redPrSum ].
<a name="docA012">
Button  build
MyLine1.x=[31,33,35,37,39,41,43,45 ... ]
MyLine1.y=[119,144,57,80,126,44,69,96 ... ]
This is for xygraph code.
Button  build
31,119
33,144
35,57
37,80
39,126
.....
Button  change above to
31,119 ; 33,144 ; 35,57 ; 37,80 ; 39,126 ...
Button  do the reverse.

<a name="docA013">
Graph program you can try
http://freeman2.com/drawdata.htm
you need adjust x-min,x-max,y-min,y-max

Graph program you can try
http://freeman2.com/cplxdraw.htm#draw02
you need adjust x-min,x-max,y-min,y-max
cplxdraw.htm#draw02 has next selection
Axes cross at x=[ 0 ], y=[ 0 ]
<a name="docA014">
If you study prime_e3.htm#bx25  for
prime 2557 to 2591, xmin=2557, xmax=2591. If
[column sum]=y value, ymin=85404, ymax=245100.
If Axes cross at x=0, y=0, all curve you get
is a tiny star at upper-right corner. If use
Axes cross at x=2550, y=100000, output graph
look better.
2017-05-03-07-45

<a name="docA015">
2017-05-03-09-45
xmin=2557, xmax=2591 and ymin=85404, ymax=245100
is far beyond common graph Axes cross at x=0, y=0
Second method to solve is to scale down. In
prime_e3.htm#bx25 click  get
MyLine1.x=[2557,2559,2561,2563,2565,2567,2569,2571,2573,2575,2577,2579,2581,2583,2585,2587,2589,2591]
MyLine1.y=[122880,210084,87176,93659,164352,113080,100308,221364,110768,91519,245100,89079,108528,186192,85404,152810,173664,86899]
goto http://freeman2.com/utility4.htm#box60 paste
122880,210084,87176,93659,164352,113080,100308,221364,110768,91519,245100,89079,108528,186192,85404,152810,173664,86899
to [Box 60, input] In [One equation] box enter
y=(x-85404)/1000
Click RUN [calculate] Output to Box 61, get
37.476,124.68,1.772,8.255,78.948,27.676,14.904,135.96,25.364,6.115,159.696,3.675,23.124,100.788,0,67.406,88.26,1.495
this is scale down y value. Do similar procedure for
2557,2559,2561,2563,2565,2567,2569,2571,2573,2575,2577,2579,2581,2583,2585,2587,2589,2591
[One equation] box enter "y=(x-2557)" output scale down x value
0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,
Draw scale down x,y value, xmin,xmax; ymin,ymax are
smaller than big value data, curve shape is the same.
2017-05-03-10-08

<a name="docA016">
pr3index()
2017-05-03-11-07
update 2017-05-03 in Real number calculator section
added sort example and run buttons ,,
It works only for numbers. Because code use
parseFloat(inp) insist input be numbers. This
version cannot sort alphabet.
2017-05-03-11-12

<a name="docA017">
2017-05-04-21-00
update 2017-05-04 add one code line
if(primeArr[k0]>columnTop)break; //a605041102
corrected bluPrAll redPrAll sum error.
If input 13, boundPrime(13) return pID=5 for 13
If input 15, boundPrime(15) return pID=6 for 17
Odd 15 sum prime upto 17 is an error.
a605041102 code stop sum at 15, get right answer.
2017-05-04-21-04

<a name="docA018">
2017-05-05-17-16
update 2017-05-05 add code from a605051620 to
a605051627. Let All given prime column sum list
background color be light blue and let
Future prime column sum list background color be
light yellow such that if reader merge given and
future two table to one, it is easy to see the
difference. One example is at
http://freeman2.com/tute0068.htm#docA118
2017-05-05-17-21

<a name="docA019">
2017-05-08-12-12
update 2017-05-08 added Date/Time and elapse to
Even meet Prime table, add same time stamp to
All given/Future prime column sum list
2017-05-08-12-18

<a name="docA020">
2017-05-20-16-15
update 2017-05-20 made minor change.
Program function is same as before.
You can find faster version of
Even Meet Prime table builder at
http://freeman2.com/prime_e4.htm#bx21
One test run get elapse seconds ratio:
Fast/Slow = 6/100 = 1.212/20.27
2017-05-20-16-20

<a name="docA021">
2017-08-04-06-55
update 2017-08-04 added selection control to
✚✚　Even meet Prime table Before update
user first click RUN 11 ☞
second click DRAW 12 ☞
Even meet Prime table show up all columns.
Liu,Hsinhan hope study primeGap2 pattern, other
gap columns buzz gap2 study. When study gap4
pattern, other gap columns buzz gap4 study.
update 2017-08-04 added following controls 
<td class=b> replace , , , , ,
replace 13 ☞ , , ,
<a name="docA022">
First click RUN 11 ☞ [gevmpr00()] ,
second click replace 13 ☞ [delList] ,
third click DRAW 12 ☞ [show Box22 table]
Before click [delList] , user can set replace
string [b,g;c,g;d,g;e,g] this string say
change <td class=b> to <td class=g>
change <td class=c> to <td class=g>
change <td class=d> to <td class=g>
change <td class=e> to <td class=g>
class=g defined to be gray color, that is delete
selected columns.
<a name="docA023">
use "b,i;c,j;d,k;e,l"
put none focus columns to fog color.
use "b,a;c,a;d,a;e,a;f,a"
change deleted columns to sea color.
use "b,aa;c,aa;d,aa;e,aa;f,aa"
change deleted columns to white color.
Here class=aa is not defined.
<a name="docA024">
Box23 define deleted prime/odd
if study gap2, click  program fill
delete list to box23. Similarly  and
fill different list to box23. User should supply
box23 delete list. Click button is a quick work.
box23 data must be odd number, must be increase.
Not listed prime/odd its color not change.

<a name="docA025">
Even meet Prime table support small primes .
Any prime theory true in general, must be true
for small primes . Study small primes first, if
find something exciting, then try develope program
extend to middle range primes. Here small primes
mean primes less than 200. Can you find any clue
worth extend to middle range primes? Liu,Hsinhan
is still playing 3,5,7.
2017-08-04-07-59

[=][][]

<a name=JavascriptIndex>
Javascript index
http://freeman2.com/jsindex2.htm   local
Save graph code to same folder as htm files.
http://freeman2.com/jsgraph2.js   local

Older Prime number and prime decomposition
http://freeman2.com/jsprime2.htm
jsprime2.htm first upload 2009-09-15

Goldbach conjecture data 6 to 1000
http://freeman2.com/tute0067.htm

Prime number study notes
http://freeman2.com/tute0068.htm

Six n Prime Table from n=1 to n=40000
http://freeman2.com/prim6n01.htm
ten table files .....
Six n Prime Table from n=360001 to n=400000
http://freeman2.com/prim6n10.htm

Prime number and prime decomposition (drawing board)
http://freeman2.com/prime_e1.htm
Chinese version 素數函數及整數之素數分解
http://freeman2.com/prime_c1.htm
prime_e1.htm first upload 2016-06-23

Even meet Prime table
http://freeman2.com/prime_e3.htm
prime_e2.htm first upload 2016-08-06
prime_e3.htm first upload 2017-04-08

Thank you for visiting Freeman's page.
Freeman Liu,Hsinhan　劉鑫漢　2017-04-01-10-08