find very easy twin prime in the infamy twin primes

[hal1se]

Originally Posted by paulunderwood

I really think you will get absolutely no where new (especially with long boring lists of computer output).

at least millions ways proof easy.
if you can think simple, and step by step.

please look simple program:

'Qbasic64 program lines
'perfect square randomize base average twin formula
'and real twin counts compare work,
'please look how very near?
'please github search,
'https://github.com/kimwalisch/primesieve/releases
'primesieve-7.1-win64-console.zip
'7.1 better performance than 7.2
'oldies sometimes goodies.
'please unzip to c:\test\
'directory.
'run qbasic64 program.
'results c:\test\tw.txt files.
'experimantal randomize test.
'n*n to (n+1)*(n+1) perfect ranges
'if we can chouse randomly, (2*n+1)/2 times two integer,
'and look: if these randomize integers are a twin prime than count=count+1
'and chousen integers not come back!
'we look every integer from n*n to (n+1)*(n+1)
'experimental count near twin count,
'near counsin count,
'near sophi dues first prime count,
'near goldbach 6k+0 count
'or near goldbach 6k+2 count *2 or near goldbach 6k+4 count*2 or
'near (goldbach 6k+2 count + goldbach 6k+4 count),
'... etc... hundreds format type dues primes alwayas near!
'randomize system mean, if we look very big results,
'not gambling, only axiomatic so formulative.
'math people if many many test randomize and prime relations,
'every body learn: primes regular base randomize so aximatic.
'math people must learn and may be make bulding:
'prime randomize system theory.
'thank you sophie.
'i am an outistic, brain damage!
'please look twin, cousin, goldbach, legendere con.
'and sophie primes alltogether, how near count?
'twin primes near positions:p2-p1=2
'sophhie primes far positions:
'p2-p1=p1+1, if p1 near 2^63 then
'p2 near 2^64
'distance: 2^63+1, astronomic!
'distance near 19 decimal digits
'but sophie due primes: first prime count near
'twin prime count!
'how?
'please look:
'https://www.quora.com/Is-the-twin-prime-problem-important
'hal ise answer, last lines important!


DIM m AS _UNSIGNED _INTEGER64
SHELL "md c:\test"
OPEN "c:\test\tw.txt" FOR OUTPUT AS #1
FOR u = 64 TO 26 STEP -.5
FOR m = INT(SQR(2 ^ u) - 2) TO INT(SQR(2 ^ u) - 18) STEP -1
CLOSE 1
y## = m
yy## = y## * y##
yy## = LOG(yy## + m + .25)
OPEN "c:\test\tw.bat" FOR OUTPUT AS #1
a$= "echo "+ "2**" + MID$(STR$(u / 2), 2) + ": " + MID$(STR$(m), 2) + "*" + MID$(STR$(m), 2)
a$=a$+ " to " + MID$(STR$(m + 1), 2) + "*" + MID$(STR$(m + 1), 2) + " >>c:\test\tw.txt"
?#1,a$
PRINT #1, "echo twin formul="; STR$(INT(1.32## * 2## * y## / yy## / yy##)); ">>c:\test\tw.txt"
a$= "c:\test\primesieve -s256 -c2 -q " + MID$(STR$(m), 2) + "*" + MID$(STR$(m), 2) + " "
a$=a$+ MID$(STR$(m + 1), 2) + "*" + MID$(STR$(m + 1), 2) + " >>c:\test\tw.txt"
?#1,a$
SHELL "c:\test\tw.bat"
NEXT
NEXT

[hal1se]

if you wonder prime number system how randomize, without any write program:

experimantal randomize test legendere con.
n=4914, near int[sqr( exp(17))]
question:
n*n to (n+1)*(n*1) range prime count?
real prime count=598
formula prime count=(2*n+1)/ln(n*n+n)=(2*4914+1)/ln(4914*4914+4914)=~578
randomize prime count:
lower bound:n*n=24147396
upper bound:(n+1)*(n+1)=24157225
sample value=2*n+1=9829
https://www.random.org/integers/?num...in&rnd=id.9829
question: how this site?
they say: true random, true? ha ha haa, this univer randoms only pesude, not ideal!
white noise, quantum random, etc..., always pseude!
if we not understand, how pseude, not important!
reality: this universe ideal random imposible!
but true mean: lengendere test ok then, true mean is true!
ctrl A
ctrl C
https://www.alpertron.com.ar/ECM.HTM
ctrl V
factor button
ctrl F
is prime
603
result 598 very near 603
may be chance
https://www.random.org/integers/?num...in&rnd=id.9830
ctrl A
ctrl C
https://www.alpertron.com.ar/ECM.HTM
ctrl R
ctrl A
ctrl V
factor
a few times (9 times) left mouse click under 1-2 cm."about this application"
ctrl F
is prim
591 very near 598
may be cahance
https://www.random.org/integers/?num...in&rnd=id.9831
ctrl A
ctrl C
https://www.alpertron.com.ar/ECM.HTM
ctrl R
ctrl A
ctrl V
factor
a few times (19 times) left mouse click under 1-2 cm."about this application"
ctrl F
is pri
582 very near 598
may be cahance!
https://www.random.org/integers/?num...in&rnd=id.9832
ctrl A
ctrl C
https://www.alpertron.com.ar/ECM.HTM
ctrl R
ctrl A
2
factor
ctrl A
ctrl V
a few times (14 times) left mouse click under 1-2 cm."about this application"
ctrl F
is p
581 very near 598
may be chance, NO!
4 different random: 4 times 9829 integer and prime count very near, randomize result.

[hal1se]

i tested two type randomize only small perfect square ranges:
https://www.random.org/integers/?num...in&rnd=id.9833

https://www.random.org/integer-sets/...in&rnd=id.9833
comma and space >> replace >> 0d0a

real twin count=48

please test yourself two type randomize near how twin count?

i don't find near 8 billions true random.
qbasic randoms very bad. < 256^3

for example:n=4294967294 perfect square:

4294967294*4294967294 to 4294967295*4294967295

how many twin real twin count = 5762802

formula twin count = 5761730

and experimental randomize test:

lower bound=4294967294*4294967294=18446744056529682436

upper bound=4294967295*4294967295=18446744065119617025

sample value=2*n+1=2*4294967295+1=8589934592

if we chouse 8589934592/2=4294967296 times so near 4 billions times two integers.
18446744056529682436 to 18446744065119617025

two type randomize data:
first:
every near 8 billions integer only one time!
18446744056529682436
18446744056529682437
18446744056529682438
...
18446744065119617024
18446744065119617025

this short squential integers mixed randomize!
mixed and mixed!
so: only mixed integers.
look 1th and 2th integers, if same time a prime then count = count+1
look 3th and 4th integers, if same time a prime then count = count+1
...
look 8589934591th and 8589934592th integers,
if same time a prime then count = count+1


chousen intgers not come back!

or:
second:
chousen integers posible come back!
18446744056529682436
to
18446744065119617025
8589934592 times frely random integers.
many many same integers this time posible!

we chouse two integers: 8589934592/2=4294967296 times
look 1th and 2th integers, if same time a prime then count = count+1
look 3th and 4th integers, if same time a prime then count = count+1
...
look 8589934591th and 8589934592th integers, if same time a prime then count = count+1

same type near result.

randomize chousen integer not come back

or

randomize chousen integer posible come back

not important!

question: randomize test count=?

count very near perfect square twin formula or real twin count or real cousin count.

count very near perfect square sophie due primes first pirme count,

count very near: perfect square near middle point symmetry point=g, goldbach 6k+0 type due symmetric prime count,


note: p1+p2 goldach dues sum primes must be:

p1>n*n

p2<(n+1)*(n+1)

for example 6k+4 goldbach dues:
g=(n*n+(n+1)*(n+1))/2
g=int[(n*n+n)]=18446744060824649730
2g=p1+p2=6k+4
2g must be 6k+4
g must be 3k+2
g=int[g/3]*3+2
g=18446744060824649732
2g=36893488121649299464
for 6k+2:
g=int[g/3]*3+1
2g=36893488121649299462

and important note for goldbach:
if p1+p2 then not count p2+p1, because same

count very near: perfect square near middle point symmetry point=g, goldbach (6k+2 + 6k+4) two type due symmetric prime count,


please test yourself, may be easy see: prime system regular base randomize, so axiomatic, so predictive, so formulative big ranges.

very clear.

how not seen prime randomize system theory in math?