[QUOTE=3.14159;240568]And, to appease Karsten;
[ATTACH]5964[/ATTACH]

1001-1360 covered.

I haven't collected for a long time. Be sure to double-check, to ensure that I did not miss any primes.[/QUOTE]

Oh, please do me a favor:

[size=+1]Stop posting your 'results' which still contain many errors and search for small primes only![/size]

Summary from above file (I've done the range 1001-1300):
[code]
missed:
3603*1048^1048+1
4527*1048^1048+1
7374*1049^1049+1
7482*1049^1049+1
7782*1049^1049+1
321*1050^1050+1
1554*1050^1050+1
2137*1050^1050+1
3235*1050^1050+1
3360*1050^1050+1
4544*1050^1050+1
7791*1050^1050+1
9934*1050^1050+1

not of the k*b^b+1 type:
252305*396^8560+1
115065*12^13450+1
102579*2^48750+1

double listed:
975*1034^1034+1
2431*1034^1034+1
4623*1034^1034+1
970*1212^1212+1
2002*1212^1212+1
2381*1212^1212+1
6093*1212^1212+1
4240*1213^1213+1
6570*1214^1214+1
7573*1214^1214+1
3421*1216^1216+1
5869*1218^1218+1
6537*1218^1218+1
6885*1218^1218+1
7102*1218^1218+1
7494*1218^1218+1
8025*1218^1218+1
3000*1219^1219+1
5142*1219^1219+1
1185*1220^1220+1
4272*1220^1220+1
8820*1220^1220+1
8973*1220^1220+1
9067*1220^1220+1
3450*1222^1222+1
6283*1222^1222+1
6510*1222^1222+1
1134*1223^1223+1
9656*1223^1223+1
642*1225^1225+1
1006*1225^1225+1
2640*1225^1225+1
3000*1225^1225+1
8716*1225^1225+1
1890*1226^1226+1
5181*1226^1226+1
1426*1227^1227+1
4750*1227^1227+1
7750*1227^1227+1
7840*1227^1227+1
1681*1228^1228+1
8880*1228^1228+1
2934*1229^1229+1
1745*1230^1230+1
2552*1230^1230+1
3112*1232^1232+1
3808*1232^1232+1
5397*1232^1232+1
5742*1232^1232+1
6616*1232^1232+1
6660*1232^1232+1
9457*1232^1232+1
9142*1233^1233+1
1424*1235^1235+1
3996*1235^1235+1
7890*1235^1235+1
3397*1236^1236+1
3834*1237^1237+1
5208*1237^1237+1
9642*1238^1238+1
[/code]

Results for b=1001-1300:
- 728 primes
- your errors: 76

-> 10.4 % error-rate!

This is not acceptable and I will [b]not[/b] trust any results of your work!

PS: I've attached my result-file.

[QUOTE=kar_bon;240587]Oh, please do me a favor:

[size=+1]Stop posting your 'results' which still contain many errors and search for small primes only![/size]

Summary from above file (I've done the range 1001-1300):
[code]
missed:
3603*1048^1048+1
4527*1048^1048+1
7374*1049^1049+1
7482*1049^1049+1
7782*1049^1049+1
321*1050^1050+1
1554*1050^1050+1
2137*1050^1050+1
3235*1050^1050+1
3360*1050^1050+1
4544*1050^1050+1
7791*1050^1050+1
9934*1050^1050+1

not of the k*b^b+1 type:
252305*396^8560+1
115065*12^13450+1
102579*2^48750+1

double listed:
975*1034^1034+1
2431*1034^1034+1
4623*1034^1034+1
970*1212^1212+1
2002*1212^1212+1
2381*1212^1212+1
6093*1212^1212+1
4240*1213^1213+1
6570*1214^1214+1
7573*1214^1214+1
3421*1216^1216+1
5869*1218^1218+1
6537*1218^1218+1
6885*1218^1218+1
7102*1218^1218+1
7494*1218^1218+1
8025*1218^1218+1
3000*1219^1219+1
5142*1219^1219+1
1185*1220^1220+1
4272*1220^1220+1
8820*1220^1220+1
8973*1220^1220+1
9067*1220^1220+1
3450*1222^1222+1
6283*1222^1222+1
6510*1222^1222+1
1134*1223^1223+1
9656*1223^1223+1
642*1225^1225+1
1006*1225^1225+1
2640*1225^1225+1
3000*1225^1225+1
8716*1225^1225+1
1890*1226^1226+1
5181*1226^1226+1
1426*1227^1227+1
4750*1227^1227+1
7750*1227^1227+1
7840*1227^1227+1
1681*1228^1228+1
8880*1228^1228+1
2934*1229^1229+1
1745*1230^1230+1
2552*1230^1230+1
3112*1232^1232+1
3808*1232^1232+1
5397*1232^1232+1
5742*1232^1232+1
6616*1232^1232+1
6660*1232^1232+1
9457*1232^1232+1
9142*1233^1233+1
1424*1235^1235+1
3996*1235^1235+1
7890*1235^1235+1
3397*1236^1236+1
3834*1237^1237+1
5208*1237^1237+1
9642*1238^1238+1
[/code]

Results for b=1001-1300:
- 728 primes
- your errors: 76

-> 10.4 % error-rate!

This is not acceptable and I will [b]not[/b] trust any results of your work!

PS: I've attached my result-file.[/QUOTE]

I said, perform a check to make sure I didn't miss any. The insults were unnecessary. I already warned that there might be errors.

[QUOTE=CRGreathouse;240581]That would be 1.[/QUOTE]

For each n.. Dammit, nevermind.

Trial division won't be necessary here. (As n increases by 1, there is one new prime added as a divisor.)

[QUOTE=3.14159;240592]Trial division won't be necessary here. (As n increases by 1, there is one new prime added as a divisor.)[/QUOTE]

Necessary? No. But it would be fastest to do trial division from prime(n+1) to about 1e8 to 1e10, except for the really small numbers.

Of course you could just do it without:
[CODE]f(n)=n=n!*primorial(prime(n));forstep(k=n+1,9e999,n,if(ispseudoprime(k),return(k\n)))[/CODE]

But I don't think that's advisable.

[QUOTE=CRGreathouse;240609]Necessary? No. But it would be fastest to do trial division from prime(n+1) to about 1e8 to 1e10, except for the really small numbers.

Of course you could just do it without:
[CODE]f(n)=n=n!*primorial(prime(n));forstep(k=n+1,9e999,n,if(ispseudoprime(k),return(k\n)))[/CODE]

But I don't think that's advisable.[/QUOTE]

I've covered every prime under 630 digits, so far.

And, 100 million? It would slow things down significantly.

As for your code, I've already defined the primorials;

p(n) = prod(1, n, prime(n)).

So, p(5) = 2 * 3 * 5 * 7 * 11 = 2310.

I've also defined n! * p(n)# as well;

fp(n) = n! * p(n).

That would simplify the code to;

f(n)=n=fp(n);forstep(k=n+1,9e999,n,if(ispseudoprime(k),return(k\n)))

[QUOTE=3.14159;240610]I've covered every prime under 630 digits, so far.

And, 100 million? It would slow things down significantly.[/QUOTE]

If you've only gone to n = 150 or so, then it's no surprise you wouldn't need much trial division yet.

[QUOTE=3.14159;240610]p(n) = prod(1, n, prime(n)).[/QUOTE]

That doesn't work; I assume you mean p(n) = prod(k=1, n, prime(k)).

Not that it matters, but this code is extremely slow:
[CODE]> p(10^5);
time = 7,070 ms.
> primorial(prime(10^5));
time = 60 ms.[/CODE]

See the Pari thread on the Software forum for the efficient code, available as either a GP script or pure Pari.

Again, I will tell you to use PFGW instead of PARI. You can do all of this with PFGW scripts or an ABC file. It would take far less time and by using the -f switch will eliminate many of the errors you are posting.

Then again the saying goes, "You can lead a blind man to water, but cannot make him drink."

[QUOTE=rogue;240630]Again, I will tell you to use PFGW instead of PARI. You can do all of this with PFGW scripts or an ABC file. It would take far less time and by using the -f switch will eliminate many of the errors you are posting.

Then again the saying goes, "You can lead a blind man to water, but cannot make him drink."[/QUOTE]

I already have an ABC script doing the work for the current collection project I'm working on.

It's collecting all primes k * (n! * p(n)#) + 1, where k is between 1 and 10000 and n between 1 and 1000; I'm only about 17% finished, and slowly growing closer to finishing up.

The -f switch is unnecessary. As n increases, a new prime is added as a divisor. It would slow progress significantly if I did so. Based on what n I'm at, at the moment, it's divisible by every prime up to 1069.

[QUOTE=rogue;240630]Again, I will tell you to use PFGW instead of PARI. You can do all of this with PFGW scripts or an ABC file. It would take far less time and by using the -f switch will eliminate many of the errors you are posting.

Then again the saying goes, "You can lead a blind man to water, but cannot make him drink."[/QUOTE]

I specifically suggested using a program like PFGW that does trial factorization (post #246).

[QUOTE=3.14159;240633]The -f switch is unnecessary. As n increases, a new prime is added as a divisor. It would slow progress significantly if I did so. Based on what n I'm at, at the moment, it's divisible by every prime up to 1069.[/QUOTE]

If you're as low as 1069 you should definitely use trial division! You could remove half the candidates just by trial-dividing up to a million.

[QUOTE=CRGreathouse;240654]If you're as low as 1069 you should definitely use trial division! You could remove half the candidates just by trial-dividing up to a million.[/QUOTE]

It would waste time and slow progress. So far, it only takes 0.023 seconds to test each candidate.