- Could someone calculate what prime numbers are before and after these

numbers:

First (R):

11621807555883689788641587458993875777666253379102712053353601884910225

29730259514945685647148706167579671158867971528164491686715212915277413

7706185638267

Second (D):

98752721695334971214618271922383690815206501681140384484657960259844385

27299469794382882275321296973244702455573996422506863560586530381700124

666716164274

Could you also explain to me how such a calculation is made?

Thanks. - unwoundgoblin wrote:

> Could someone calculate what prime numbers are before and after these

R-238, R+750, D-101, D+23.

> numbers:

>

>

> First (R):

> 11621807555883689788641587458993875777666253379102712053353601884910225

> 29730259514945685647148706167579671158867971528164491686715212915277413

> 7706185638267

>

> Second (D):

> 98752721695334971214618271922383690815206501681140384484657960259844385

> 27299469794382882275321296973244702455573996422506863560586530381700124

> 666716164274

> Could you also explain to me how such a calculation is made?

There is no practical "direct" way to compute it.

You have to eliminate all candidates by finding a factor

or performing a primality or PRP (probable prime) test.

See e.g. http://primes.utm.edu/prove/index.html

When a PRP is found, you (usually for this kind of problem)

have to prove it prime with a relatively slow general

method like APR-CL or ECPP.

For numbers of your size, a computer program is needed.

I used PARI/GP and recommend it. My work for the prime after R:

(16:42) gp > nextprime(R)-R

%63 = 750

(16:42) gp > isprime(R+750)

%64 = 1

nextprime computes a prp. The much slower isprime makes a primality proof.

--

Jens Kruse Andersen - unwoundgoblin wrote:
> Could someone calculate what prime numbers are before and after these

As Jens correctly stated, there's not a (known) formula to find the

> numbers:

>

> First (R):

> 11621807555883689788641587458993875777666253379102712053353601884910225

> 29730259514945685647148706167579671158867971528164491686715212915277413

> 7706185638267

>

> Second (D):

> 98752721695334971214618271922383690815206501681140384484657960259844385

> 27299469794382882275321296973244702455573996422506863560586530381700124

> 666716164274

>

> Could you also explain to me how such a calculation is made?

next prime. It's relatively easy to brute-force it, though, simply by

counting up or down from the number and running a primality test. For

your information, here's a very simple Frink program that does the same,

at least in one direction:

R=[your number]

r = r

while(! isPrime[r]) // While not prime

r=r+2

println[r]

Frink's isPrime does probable-prime test, but against a large number

of bases. Enough bases that the probability of your hardware failing

during the calculation (and you winning the lottery and getting struck

by lightning at the same time) is much, much higher. Unfortunately, I

don't have a primality-proving routine yet.

Frink documentation:

http://futureboy.us/frinkdocs/

--

Alan Eliasen | "When trouble is solved before it

eliasen@... | forms, who calls that clever?"

http://futureboy.us/ | --Sun Tzu > As Jens correctly stated, there's not a (known) formula to find the

For numbers of this size, it's also possible to plug them into Dario

> next prime.

Alpern's java applet with the N() and B() function for next and previous.

http://www.alpertron.com.ar/ECM.HTM

William

Poohbah of OddPerfect.org