I'm guessing it will continually overflow until it reaches the necessary trial factoring limit.

[QUOTE=Charles]So how long do you expect it to take, compared to your earlier efforts?
[/QUOTE]

About 400-700 times as long as the previous effort. The previous effort took about 10 minutes. This is going to take 2-3 days.

I'm abandoning this one. It is too long and too costly. I have inadequate comp power to outbest the number you submitted anytime soon.

I'm going back to looking for larger primes.

[QUOTE=3.14159;228833][code]
P.S: Can someone prove the primality of the number 29201806527798202690471270497026289647897695441591089473790387382190437432352472117744280333628938004491474620381040060030880069981
using trial factoring alone?
[/code][/QUOTE]

It depends on the definition of "trial factoring alone." I can easily prove that it is prime where the only factoring done is trial factoring - does that count as "trial factoring alone?"

(Generate an N-1 proof. Trial factoring will easily completely factor N-1, and no other factoring is necessary to complete the proof).

[QUOTE=3.14159;228858]About 400-700 times as long as the previous effort. The previous effort took about 10 minutes. This is going to take 2-3 days.

I'm abandoning this one. It is too long and too costly. I have inadequate comp power to outbest the number you submitted anytime soon.[/QUOTE]

I'm hoping to submit a number so large that you won't even bother trying to top it. I estimate that my current number would take you 3-5 months.

[QUOTE=CRGreathouse;228846]Pi, I started work on a second number as soon as I finished the first. Your number shouldn't take too long, so you'll probably get a record before I smash it. :smile:



Good luck. If you find an answer, post it -- and tell me if mine is OK.[/QUOTE]

best I found so far :


[B][U]General Rules[/U][/B]
1. Has no factors below 2^30<- replace with step 2 of trial factor for trial factored primes.
2. Passes a pseudoprimality test (Recommendation: 1-3 bases)
3. Is not a "small" prime. (Please ensure it is ≥ 1000 digits.)

[B][U]Trial factor[/U][/B]
Step 1. Pick a number.
Step 2. Trial division up to its square root.
Step 3. If prime, report here.

[B][U]Categories[/U][/B]
1. Generalized Proths, where b is any integer.
i.Proths, where b is 2.
ii.Proths, where b is a factorial number.
iii.Proths, where b is a primorial number.
iv.Proths, where b is a prime number.
2. Primorial, k * p(n) + 1
3. Factorial, k * n! + 1
4. Generalized Cullen/Woodall, k * b^k + 1
i.Factorial Cullen/Woodall, where b, optionally k, is a factorial number.
ii.Primorial Cullen/Woodall, where b, optionally k, is a primorial number.
iii.Prime-based Cullen/Woodall, where b is a prime number
5. k-b-b, numbers of the form k * b^b + 1
i.Factorial k-b-b, where b, optionally k, is a factorial number.
ii.Primorial k-b-b, where b, optionally k, is a primorial number.
iii.Prime-based k-b-b, where b is a prime number.
6. Number, square, and fourth, where n^1 + 1, n^2 + 1, and n^4 + 1 are all primes.
7. Special Cofactor, where the prime cofactor is of one of the forms used in this list.
8 .General Cofactor, where the prime cofactor is not of a special form.
9. General arithmetic progressions, k * b^n + c, where c is a prime > 10^2, where the prime is at least 2000 digits in length, and where the exponent n > 1.
10. Obsolete-tech-proven primes, using the original PrimeForm or Proth.exe, or any other prime to prove primality of any type of prime listed here. Note: The prime must be at least 7500 digits in length.
11 .N-1 analogues of items in 1.
a. k>1 for the analogue of 1i
12. N-1 analogues of items 2 and 3.
13. N-1 analoges of items 8-11.
14. N-1 analogues of items 12-15.
15. Obsolete-tech-proven primes, for -1 analogues only.
16. Twins.

arithmetic progressions
Every odd prime is indeed part of an arithmetic progression, either 2n + 1, or 6n ± 1. It's in fact impossible for an odd prime not to be in an arithmetic progression.

no fermats or mersennes

no special form primes -> Yes, they are all special-form primes.

okay technically if I did my research proper all until 5iii can go under 1

[QUOTE=science_man_88]okay technically if I did my research proper all until 5iii can go under 1
[/QUOTE]

Cullen-Woodalls are not Proths. What a load of :poop:

though Wikipedia says k*2^n+1 not k*b^n+1

[QUOTE=science_man_88]though Wikipedia says k*2^n+1 not k*b^n+1
[/QUOTE]

Sorry, buddy, you debunked yourself.

[QUOTE=Chris Caldwell]Though actually not a true class of primes, the primes of the form k * 2[sup]n[/sup]+1 with 2[sup]n[/sup] > k are often called the Proth primes.[/QUOTE]

[QUOTE=3.14159;228876]Cullen-Woodalls are not Proths. What a load of :poop:[/QUOTE]

not what Wikipedia is saying :

The Cullen numbers are the special case of Proth numbers with k = n.
The Fermat numbers are a special case of the Proth numbers with k = 1.

Woodalls no Cullens unless i misinterpret what is said are.

[QUOTE]Proths, where b is 2. [/QUOTE]

Wikipedia is saying Proth = k*2^n+1 so b=2 is general specification according to that.

[QUOTE=science_man_88]not what Wikipedia is saying :

The Cullen numbers are the special case of Proth numbers with k = n.
The Fermat numbers are a special case of the Proth numbers with k = 1.

Woodalls no Cullens unless i misinterpret what is said are.[/QUOTE]

Lie by omission, you did not include that [B]b = 2[/B].

Where b != 2, it is Generalized Cullen-Woodalls, which are on the list, which are not Proth numbers, which is where [B]b = 2.[/B]

The categories of my list remain at 26, 20 of which I will search for.