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Old 2018-08-27, 09:12   #12
hal1se
 
Jul 2018

3×13 Posts
Default not important rough formula, important question: how is regularly?

range: int[exp(43)]-2e12 to int[exp(43)]+2e12
4727837468229346561 to 4727841468229346561
range:4 trillion, 19 decimal digit, real positive integer.

ln(middle point of range)=43
7tuplet rough range count=?56*4*1e12/43^7=824
(oeis.org/A022009)) septuplet mean: 30n+11, 30n+13, 30n+17, 30n+19, 30n+23, 30n+29, 30n+30+1
real septuplet count:815
815 very near 824, but not lower limit, only rough count!
_________
range: int[exp(41))-2e12 to int[exp(41)]+2e12
range: 639841493530054949 to 639845493530054949
range:4 trillion, 18 decimal digit, real positive integer.

ln(middle point of range)=41
7tuplet rough range count=? 56*4*1e12/41^7=1150
real septuplet count:1141
1150 very near 1141
__________
range: int[exp(39)]-2e12 to int[exp(39)]+2e12
range: 86591400423993746 to 86595400423993746
range:4 trillion, 17 decimal digit, real positive integer.

ln(middle point of range)=39
7tuplet rough range count=? 56*4*1e12/39^7=408*4=1632
7tuplet real count=1600
1600 very near 1632
___________
range: int[exp(36)]-2e12 to int[exp(36)]+2e12
range: 4309231547115195 to 4313231547115195
range:4 trillion, 16 decimal digit, real positive integer.

ln(middle point of range)=36
7tuplet rough range count=? 56*4*1e12/36^7=2858
7tuplet real count=2764
2858 near 2764, but not very near!
____________
range: int[exp(33)]-2e12 to int[exp(33)]+2e12
range: 212643579785916 to 216643579785916
range:4 trillion, 15 decimal digit, real positive integer.

ln(middle point of range)=33
7tuplet rough range count=? 56*4*1e12/33^7=5255
7tuplet real count=5122
5255 near 5122
____________

exp(n): if n is not integer?
range: int[exp(30,3)]-2e12 to int[exp(30,3)]+2e12
range: 12425231835807 to 16425231835807
range:4 trillion, 14 decimal digit, real positive integer.

ln(middle point of range)=30,3
7tuplet rough range count=? 56*4*1e12/(30,3)^7=9533
7tuplet real count=9308
9533 near 9308
_______________

all ranges: 4 trillion fix range. if numbers goes to big numbers, septuplet real counts goes to small numbers, because range fix!
_______________
question:
exp(n-0,5) to exp(n+0,5) ranges real septuplet count?
_______________
range: 0 to int[exp(27,5)]
range: 0 to 877199251318
ln(middle point of range): ln((exp(27,5))/2)=26,806852819439182678541554041555
56*exp(27,5)/(26,806852819439182678541554041555)^7=4938
real culumaltive septuplet count=5539
not very near, only near, and cumulative septulet rough count is lower limit allways! (if n>30 then)
_________
range: exp(28-+0,5)

range:877199251318 to 2384474784797
note: exp(27,5) to exp(28,5) middle point not exp(28) of course, but near!
my calculation only rough!
56*exp28/28^7=6002 rough count appr.
real 7tuplets count= 5810
not very near but only near and not lower limit result!
important: ( 0 to exp(27,5) septuplet cumulative count) < (exp(27,5) to exp(28,5) range septuplet count)
if n>30 then, n is an integer or not:
every exp(n-+0,5) range septuplet count > (0 to previous range cumulative count)
so infnity septuplet there are.
every septuplet contain 3 twin prime, so infinity twinprime there are!
this is not math proof!
only look full picture.
_________
range: exp(29-+0,5)
range:2384474784797 to 6481674477934
56*exp29/29^7=12762
real 7tuplets count: 12694
very near but not lower limit!
_____________
range: exp(30-+0,5)

range:6481674477934 to 17619017951355
56*exp30/30^7=27363
real septuplet count=27179
very near result!
_______________
range: exp(31-+0,5)

range:17619017951355 to 47893456332463
56*exp31/31^7=59126
real septuplet count=58592
very near result!

this rough counts, and rough count formulas, not important!
important question: how is it every prime template's direct elements groups regularly?

for example:
how is regularly?,
7 prime same time group:30n+11, 30n+13, 30n+17, 30n+19, 30n+23, 30n+29, 30n+30+1
if, math people:
this every prime template's direct elements groups regularly, proofed near future,
very simple bottom lines:

range:exp(N-0,5) to exp(N+0,5)

exp(1e6-+0,5) rough septuplet count?
A=56*exp(1e6)/(1e6)^7
exp(1e6+1-+0,5) rough septuplet count?
B=56*exp(1e6+1)/(1e6+1)^7
((1e6+1)^7/(1e6)^7)=1,000007000021000035000035000021e+42/1e42=1,000007000021000035000035000021...
B/A=
=exp(1)/1,000007000021000035000035000021
=2,7182628...
_2,7182818284590452353602874713527... :real exp(1)

exp(1e9-+0,5) rough septuplet count?
C=56*exp(1e9)/(1e9)^7
exp(1e9+1-+0,5) rough septuplet count?
D=56*exp(1e9+1)/(1e9+1)^7
(1e9+1)^7/(1e9)^7=1,000000007000000021000000035e+63/1e+63
=1,000000007000000021000000035000000035000000021...
D/C=exp(1)/1,000000007000000021000000035000000035000000021...
=2,718281809...
_2,7182818284590452353602874713527... : real exp(1)

note: number <exp(30) then septuplet big fluctations!
for example:
exp(29-+0,5) septuplet count / exp(28-+0,5) septuplet count=12694/5810=2,18485...>exp(1)
but:
exp(30-+0,5) septuplet count / exp(29-+0,5) septuplet count=27179/12694
=2,141.. <exp(1)
exp(31-+0,5) septuplet count / exp(30-+0,5) septuplet count=58592/27179
=2,15578... <exp(1)
if numbers < exp(30) then septuplets count big fluctations,
but, for example numbers > exp(1e6) then sextuplets count very regularly and fluctations very small!
good by everyone, my brain fault again, i am going to ...
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Old 2018-08-27, 13:40   #13
CRGreathouse
 
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Aug 2006

174916 Posts
Default

Sorry, I can't make any sense of this.
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