[QUOTE=science_man_88;233214]is there a formula for telling which in a lucas sequence are prime ?[/QUOTE]

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?

[QUOTE=CRGreathouse;233224]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?[/QUOTE]

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.

[QUOTE=science_man_88;233229]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.[/QUOTE]

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

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

something new ?
 

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

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.

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[/code]

Roughly [TEX]\frac{2e^{-\gamma}}{\log10^{30}}\approx1.6\%[/TEX].

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.

[QUOTE=Charles;233663]Roughly [TEX]\frac{2e^{-\gamma}}{\log10^{30}}\approx1.6\%[/TEX].[/QUOTE]

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

[QUOTE=3.14159;233800]Even though there are more potential factors ≥ 1000000000000000000000000000057 than there are of the lesser primes?[/QUOTE]

Correct. In fact, more than 30% of numbers have no prime factors greater than their square root. Think about it: there more than 90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 [i]times[/i] 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.

[QUOTE=Charles;233803]Correct. In fact, more than 30% of numbers have no prime factors greater than their square root. Think about it: there more than 90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 [i]times[/i] 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.[/QUOTE]

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