Thread for posting tiny primes

[3.14159]

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

Originally Posted by Charles

So how long do you expect it to take, compared to your earlier efforts?

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.

[wblipp]

Originally Posted by 3.14159

P.S: Can someone prove the primality of the number 29201806527798202690471270497026289647897695441591089473790387382190437432352472117744280333628938004491474620381040060030880069981 
using trial factoring alone?

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).

[CRGreathouse]

Originally Posted by 3.14159

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 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.

[science_man_88]

Originally Posted by CRGreathouse

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.



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

best I found so far :


General Rules
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.)

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

Categories
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.

[science_man_88]

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

[3.14159]

Originally Posted by science_man_88

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

Cullen-Woodalls are not Proths. What a load of

[science_man_88]

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

[3.14159]

Originally Posted by science_man_88

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

Sorry, buddy, you debunked yourself.

Originally Posted by Chris Caldwell

Though actually not a true class of primes, the primes of the form k * 2ⁿ+1 with 2ⁿ > k are often called the Proth primes.

[science_man_88]

Originally Posted by 3.14159

Cullen-Woodalls are not Proths. What a load of

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.

[science_man_88]

Proths, where b is 2.

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

[3.14159]

Originally Posted by 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.

Lie by omission, you did not include that b = 2.

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

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