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Old 2020-05-30, 18:36   #1
Godzilla
 
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May 2016

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Default f(n+6)= (n^2-1*(4*n+5))=N

Good evening,

The particular progression relation of this function n + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6.... generates successively prime and composite numbers which are connected to the next and previous function f(n+6)

I tried with large numbers but ... does anyone have an opinion please?

This Function f(n+6):

f(n+6)= (n^2-1*(4*n+5))=N


\frac{N}{n+1}=

odd integer prime number or composite number

Example:


n = 6

f(n) = N = 7

factor = 7=1*7

NOTE : \frac{N}{n+1}= \frac{7}{6+1}=1


n = 12

f(n) = 91

factor = 91=1*7*13

NOTE : \frac{N}{n+1}= \frac{91}{12+1}=7


n = 18

f(n) = 247

factor = 247=1*13*19

NOTE : \frac{N}{n+1}= \frac{247}{18+1}=13



n = 24

f(n) = 475

factor = 475=1*5*5*19

NOTE : \frac{N}{n+1}= \frac{475}{24+1}=19


n = 30

f(n) = 775

factor = 775 =1*5*5*31

NOTE : \frac{N}{n+1}= \frac{775}{30+1}=25


n = 36

f(n) = 1147

factor = 1147=1*31*37

NOTE : \frac{N}{n+1}= \frac{1147}{36+1}=31


n = 42

f(n) = 1591

factor = 1591=1*37*43

NOTE : \frac{N}{n+1}= \frac{1591}{42+1}=37


n = 48

f(n) = 2107

factor = 2107=1*7*7*43

NOTE : \frac{N}{n+1}= \frac{2107}{48+1}=43


n = 54

f(n) = 2695

factor= 2695=1*5*7*7*11

NOTE : \frac{N}{n+1}= \frac{2695}{54+1}=49


n = 60

f(n) = 3355

factor = 3355=1*5*11*61

NOTE : \frac{N}{n+1}= \frac{3355}{60+1}=55


n = 66

f(n) = 4087

factor = 4087=1*61*67

NOTE : \frac{N}{n+1}= \frac{4087}{66+1}=61


n = 72

f(n) = 4891

factor = 4891=1*67*73

NOTE : \frac{N}{n+1}= \frac{4891}{72+1}=67


n = 78

f(n) = 5767

factor = 5767=1*73*79

NOTE : \frac{N}{n+1}= \frac{5767}{78+1}=73


n = 84

f(n) = 6715

factor = 6715=1*5*17*79

NOTE : \frac{N}{n+1}= \frac{6715}{84+1}=79


n = 90

f(n) = 7735

factor = 7735=1*5*7*13*17

NOTE : \frac{N}{n+1}= \frac{7735}{90+1}=85


n = 96

f(n) = 8827

factor = 8827=1*7*13*97

NOTE : \frac{N}{n+1}= \frac{8827}{96+1}=91
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Old 2020-05-30, 20:21   #2
kar_bon
 
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Quote:
Originally Posted by Godzilla View Post
[...] generates successively prime and composite numbers [..]
Why? Because...
Quote:
Originally Posted by Godzilla View Post
f(n+6)= (n^2-1*(4*n+5))=N
N = n2 - 4n - 5 = (n-5)*(n+1), so your N/(n+1) = n-5.

So your composite/prime generator f(n) = n-5.
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Old 2020-05-31, 06:55   #3
VBCurtis
 
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Quote:
Originally Posted by kar_bon View Post
Why? Because...


N = n2 - 4n - 5 = (n-5)*(n+1), so your N/(n+1) = n-5.

So your composite/prime generator f(n) = n-5.
Soooo.... f(n+6) would be.... n + 1?

Awesome. Godzilla, indeed.
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Old 2020-05-31, 07:16   #4
Batalov
 
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Mar 2008
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Quote:
Wolfgang Mozart: I never knew that music like that was possible!
...

Wolfgang Mozart: No, no! One hears such sounds, and what can one say but... "Salieri."
.
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