Build primeA6n[] list and build primeGap[] .

Even meet Prime table a604011006 update 2017-05-20

Goldbach conjecture. integer to prime summation ; gevmpri0

freeman2.com/prime_e2.htm 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

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 ,

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

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 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()]

yellow input, BoxPGR output, [Allowed?] read one line gap sequence.

✚✚ Click RUN14 four buttons first, click RUN5

for prime gap mod(6)=0,2,4 and consecutive n count.

define fake prime table see why squares cannot replace prime?

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

[gap difference] that is gap up/down list. same list also in Box02

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)

http://freeman2.com/gevmpri0.jpg and gevmpri1.jpg use

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]

✚✚ 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.

This is html table code graph. prime_e3.htm main topic.

✚✚

from 102=89+13 to 102-89-13 and evaluate to 0. Confirm 102=89+13 is OK.

<a name="program0">

**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
**

Consecutive Prime Gaps 10,10 allowed? or not allowed? Please input and test.

Next yellow box INPUT Prime Consecutive Gaps , click Example buttons.

Example ,,,, ; ,,,, ; [,,,]

yellow input, BoxPGR output

prime 5,7,11 cut

exam prime from prime 5 to prime expect a small prime for [prime5cut()]

BoxPGR

yellowbox example , , , , ; prime 5 to prime

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

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

BoxPGA Yellow is one series calculation, green is another

QEboxcPGA.value='' ;

BoxPGA input

<a name="bxPGB"> click [modsix024 ], build modsix024[] array first.

Compact [modsix024] data, input from modsix024[]

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,

BoxPGC ;

QEboxcPGC.value=''

QEspanPrimeCount.innerHTML='' ;

QEspanascend024.innerHTML='' ;

list024 example

Prime gap modsix begin/end

BoxPGD ; ask list024

QEboxcPGD.value='';

,

Box04:input integer factorization list, click [Prime counting] Box05:output summary

Box01 ; paste user prime list to Box01 or prime list

in Box02 Show primeID , prime , gap , gap%6 , gapUp/Down , 6*n±1

Box02 data column ↕ to ↔ row change ,

upper_lower bounds , default number 1 to 5001

Box02 ;

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

[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: , , ,

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 ...

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

QBboxc07.value='' ;

[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=''

[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

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

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

[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.

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='' ;

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?

or Click [prime sum seq.] input Integer upper/lower bounds silver box, output Box15.

Box14 Prime sum random 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 silver box sequential input, output to Box15.

6*n±1 ? [Whitelane] output primeID

Box15 Prime sum output [Detail], [Pave] debug? debug slow down.

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

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>

6*n-1 prime. Output to Box18.

example , Box17 input Box18 output

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 |

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 , , , , , ,

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 |

Box22 output ;

QDboxc22.value='' ;

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

Box24 output ;

INPUT bgn , end

Ex. , , , , , ;

Box25 output ; Help , ; unknown future column sum

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

Box81

Box81 input Box82 output , , , ♫

Box82 ; ; , ,

Integer ends= ; ,

QPboxc82.value='' ;

[=][=]

<a name="docA001"> update 2017-04-11 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 allor other choice and(8)23 yesor not. If click [ all ] box, program change to [prime] then change to [b:6n-1] to [c:6n+1] to [delPrim] If choosekeep primegraph output only prime column. <a name="docA002"> What is "prime column" ? In next graphBottom 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)

_ _ _ _ _ _ prime13 _ _ _ _ _ _ prime11 _ _ # $ _ _ prime07 _ _ _ _ _ _ prime05 _ _ _ $ _ _ prime03 03 05 07 09 11 13 primGap _ _ _ _ _ _ x-axis keep primechoice 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 yesor 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,;add ,,, Above added [even],[odd],[eo],[oe]. Please see 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"> 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 sectionDRAW ☞

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 update 2017-05-03 addedunknown 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"> 2017-05-03-07-11 update 2017-05-03 addedx 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"> 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 [=][][]

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Older Prime number and prime decomposition

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