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-   -   Continued Fraction of Primes (https://www.mersenneforum.org/showthread.php?t=470)

Cyclamen Persicum 2003-03-26 12:52

Continued Fraction of Primes
 
If one knows
x=1/(2 + 1/(3 + 1/(5 +1/(7 +1/(11 ...,

he can easily produce the list of all primes,
but what does x equal to by itself?

eepiccolo 2003-03-26 13:37

0.4323
3208718590 2868909253 7932419999 6370511089 6877651310
3281520671 5855390511 5295886642 4773023467 5307312901
3588747517 1102192547 3474173059 9816815325 2537010284
6860319246 0457044667 2860224884 0679362020 1938436437
9879295524 6786129609 7638935269 4027752231 9731978458
6355957940 3620206633 8633654544 8951089096 5971586278
7332585763 6862001836 7995212808 7865043794 6101266432
6042252640 0822552675 2215113354 1703783531 9471839...


[b]Works Cited[/b]

"Prime Curios!"
[url]http://primes.utm.edu/curios/page.php?number_id=2750[/url]

Cyclamen Persicum 2003-03-27 13:41

That is fake!
Is it possible to calculate the fraction
without the beforehand knowing of all primes ?

eepiccolo 2003-03-27 14:30

[quote="Cyclamen Persicum"]That is fake!
Is it possible to calculate the fraction
without the beforehand knowing of all primes ?[/quote]

You know, you've put a lot of weird stuff on the forums recently, and as far as I know, no one has blatantly yelled at you or called your stuff fake. Some courtesy would be appreciated.

cheesehead 2003-03-27 15:58

[quote="Cyclamen Persicum"]Is it possible to calculate the fraction without the beforehand knowing of all primes ?[/quote]
Yes, it is.

Have you ever studied infinite series in a math class? There are techniques for calculating the sum of an infinite series once the general formula for each term is known, even though not all the specific values are known. Continued fractions can be similarly calculated.

Cyclamen Persicum 2003-03-29 07:16

[quote]Have you ever studied infinite series in a math class[/quote]

That's a merely declaration and an empty sound.
None can give a form for n-member of such kinda series, which
convergence to continued fraction of all primes.

cheesehead 2003-03-29 13:13

Okay, you're right. It's not possible. The number is fake. I was blowing smoke, and you called me on it.

trif 2003-03-29 19:27

:rolleyes: I guess he can take it up with Michael Hartley now.

eepiccolo 2003-03-30 02:19

[quote="cheesehead"]Okay, you're right. It's not possible. The number is fake. I was blowing smoke, and you called me on it.[/quote]

I still belive in you Mr. llama cheesehead sir!

wpolly 2003-04-13 14:56

Consider the continued fration
x=1+1/(2+1/(3+1/(4+1/(.........

I've calculated the value of x and got this result:
[code:1]x=1.4331274267 2231175831 7183455775 9918204315
1276790598 0523434428 6363943091 8325417290 0136503726
4357861146 5950013404 3088536429 5301770827 3894637360
4073219525 3363524736 8315637151 3409658626 2656344480
856171979[/code:1]

Is there a formula of the exact x value now?[/code]


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