PARI's commands - Page 137

CRGreathouse · 2010-10-12, 16:53

Quote:

Originally Posted by science_man_88

is there a formula for telling which in a lucas sequence are prime ?

Sure, take any of the standard formulas for prime-testing and substitute the formula for a member of the Lucas sequence for the number.

But that would be very slow. Are you looking for an algorithm instead?

science_man_88 · 2010-10-12, 17:34

Quote:

Originally Posted by CRGreathouse

Sure, take any of the standard formulas for prime-testing and substitute the formula for a member of the Lucas sequence for the number.

But that would be very slow. Are you looking for an algorithm instead?

my latest idea if no prime finding formula that can work fast can be found is to create something that will feed the exponents into findrec in specific possible orders increasing that may find multiple lucas sequences I'm unsure right now though.

CRGreathouse · 2010-10-12, 18:29

Quote:

Originally Posted by science_man_88

my latest idea if no prime finding formula that can work fast can be found is to create something that will feed the exponents into findrec in specific possible orders increasing that may find multiple lucas sequences I'm unsure right now though.

Well, you have the code... try it!

science_man_88 · 2010-10-14, 00:37

might need to rethink lol 39! possible for 39 and then 39!/2! for 38 etc. lol

science_man_88 · 2010-10-17, 23:47

Code:

for(i=2,#mersenne,print(isprime(floor(mersenne[i]^exp(1)/mersenne[i-1]))))

gives me false consistently, care to see if it's done already ? etc. I think someone else got in my account as I don't remember adding an image.

3.14159 · 2010-10-18, 02:13

I was just pondering..

Imagine you choose a random 210-digit odd number to factor.

What are the odds that it has no factor ≤ 30 digits ?

Ex:

Code:

765223385698389926571242942756698700016608850019007376399764250461012579493486533505154279222065824923099207583225846866415511389377654307908279943765426193326813047827405221065725982667368472098358003394603467 = 77771442250823086981801725238987802825302970789365898005146018089 * 9839387872356080094484924867666017102610781172377705317233177547076926514496969631181594854116446488590453712956846616476891085418145551273102803

CRGreathouse · 2010-10-18, 04:55

Roughly $\frac{2e^{-\gamma}}{\log10^{30}}\approx1.6\%$ .

science_man_88 · 2010-10-18, 12:39

I find that exp(1) seems to work in numerous places I tried Pi in the same places and it didn't always turn out false.

3.14159 · 2010-10-19, 00:53

Quote:

Originally Posted by Charles

Roughly $\frac{2e^{-\gamma}}{\log10^{30}}\approx1.6\%$ .

Even though there are more potential factors ≥ 1000000000000000000000000000057 than there are of the lesser primes?

CRGreathouse · 2010-10-19, 01:10

Quote:

Originally Posted by 3.14159

Even though there are more potential factors ≥ 1000000000000000000000000000057 than there are of the lesser primes?

Correct. In fact, more than 30% of numbers have no prime factors greater than their square root. Think about it: there more than 90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 times as many primes between 1e10 and 1e100 as between 1 and 1e10, and yet 30% of the numbers near 1e100 use none of those many large primes.

3.14159 · 2010-10-19, 01:25

Quote:

Originally Posted by Charles

Correct. In fact, more than 30% of numbers have no prime factors greater than their square root. Think about it: there more than 90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 times as many primes between 1e10 and 1e100 as between 1 and 1e10, and yet 30% of the numbers near 1e100 use none of those many large primes.

This statement can be distorted into some strange sort of crackpottery about some obscure pseudo-proof about some obscure pseudo-theorem.

2010-10-17, 23:47	#1501
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶×131 Posts	something new ? Code: for(i=2,#mersenne,print(isprime(floor(mersenne[i]^exp(1)/mersenne[i-1])))) gives me false consistently, care to see if it's done already ? etc. I think someone else got in my account as I don't remember adding an image. Last fiddled with by science_man_88 on 2010-10-17 at 23:52

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2010-10-14, 00:37	#1500
science_man_88 "Forget I exist" Jul 2009 Dumbassville 10000011000000₂ Posts	might need to rethink lol 39! possible for 39 and then 39!/2! for 38 etc. lol

2010-10-18, 04:55	#1503
CRGreathouse Aug 2006 3×1,993 Posts	Roughly $\frac{2e^{-\gamma}}{\log10^{30}}\approx1.6\%$ .

2010-10-18, 12:39	#1504
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶·131 Posts	I find that exp(1) seems to work in numerous places I tried Pi in the same places and it didn't always turn out false.