Numbers & such

[H:O:R:A:C:E]

sika = [(prime -2)/(prime)]!

as the prime values increase, the multiplier terms approach a value of one. this will alter the value to a lesser degree as the terms progress.

i would like a symbol much like phi to indicate this value, but with an additional vertical line (parallel) ... making it symmetrical:

[H:O:R:A:C:E]

Fiddler on the Roof (1971), Sunrise, Sunset:

https://www.youtube.com/watch?v=nLLEBAQLZ3Q

[H:O:R:A:C:E]

The First 10,000 Primes: https://primes.utm.edu/lists/small/10000.txt

as we add terms, the approximate value of sika diminishes, but in a less and less dramatic fashion... tending towards a "stable" value which is greater than zero.
here are the values i've obtained for the beginning prime "steps" in the process:
2-skipped
3- 0.3333
5- 0.2000
7- 0.14285
11- 0.11688
13- 0.09890
17- 0.08726
19- 0.07807
23- 0.07129
29- 0.06637
31- 0.05202
37- 0.04921
41- 0.04681
43- 0.04463
47- 0.04273
53- 0.04112
59- 0.03972
61- 0.03842
67- 0.03727
71- 0.03622
73- 0.03523
79- 0.03434
83- 0.03351
89- 0.03276
97- 0.03208
101- 0.03145
103- 0.03084
107- 0.03026
109- 0.02970
113- 0.02918
127- 0.02872

after just thirty terms, we've determined that the percentage of prime pairs within the set of odd pairs is less than 3%.

[H:O:R:A:C:E]

i woulda liked to have had someone help me out here.
i'll wrap up asap.

[H:O:R:A:C:E]

sorry, i've been too ill to do a recap.
i think the majority of ideas got exposed though.
namaste.

[H:O:R:A:C:E]

oh snap, i've remembered one last important bit.
after establishing the fractional relationship of (sopp) to (soop),
that value is used to solve the other ratios for k values in Polignac's conjecture.
wikipedia: Polignac's conjecture from 1849 states that for every positive even natural number k,
there are infinitely many consecutive prime pairs p and p′ such that p′ − p = k (i.e. there are infinitely many prime gaps of size k).
The case k = 2 is the twin prime conjecture.

for the prime pairs (k=2), the percentage is sika.
[k values are never odd, since "prime" + "odd" is always "even", which cannot be a prime (ie, divisible by 2)]
when k=4, the percentage is the same.
at k=6,(the so-called "sexy primes") making for pairs of (k, k+6), the prime of "3" is only half as effective at eliminating these pairs...
this is because "3" will factor into each of the terms when it factors into the other (but NOT k+1 nor k+7, and NOT k+2, nor k+8;
but again YES at k+3 and k+9, etc).
primes of the nature (k, k+8) should be found as commonly as twin primes (sika valued). primes of the nature (k, k+10)
shall be found to be half as effectively diminished by the prime factor "5"; and etc.

It would be 2039.

[Miss Hepburn]

Originally Posted by Glenda

It would be 2039.

Hi, who are you talking to and what is this in answer to? Thank you.