Continued Fraction of Primes

Cyclamen Persicum · 2003-03-26, 12:52

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...

Works Cited

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

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:

Originally Posted by Cyclamen Persicum

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

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:

Originally Posted by Cyclamen Persicum

Is it possible to calculate the fraction without the beforehand knowing of all primes ?

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

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

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

eepiccolo · 2003-03-30, 02:19

Quote:

Originally Posted by cheesehead

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

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]

2003-03-26, 12:52	#1
Cyclamen Persicum Mar 2003 3⁴ Posts	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?

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2003-03-26, 13:37	#2
eepiccolo Dec 2002 Frederick County, MD 2×5×37 Posts	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... Works Cited "Prime Curios!" http://primes.utm.edu/curios/page.php?number_id=2750

2003-03-27, 13:41	#3
Cyclamen Persicum Mar 2003 3⁴ Posts	That is fake! Is it possible to calculate the fraction without the beforehand knowing of all primes ?

2003-03-29, 13:13	#7
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 2²×3×641 Posts	Okay, you're right. It's not possible. The number is fake. I was blowing smoke, and you called me on it.

2003-03-29, 19:27	#8
trif Aug 2002 2·101 Posts	I guess he can take it up with Michael Hartley now.

2003-04-13, 14:56	#10
wpolly Sep 2002 Vienna, Austria 3×73 Posts	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]