[QUOTE=kar_bon]Less primes to find among the remaining candidates!

Example: k*2^n-1

n-range: 600000-1000000
sieved to p=26*10^12
k=337: 2618 candidates left
k=315: 32276 candidates left

Primes in that range found:
k=337: none
k=315: 3[/QUOTE]

Ah, I see what the problem is: You assumed I did n-range searches. I perform k-range searches, which means I search for primes in arithmetic progressions.

Maybe this clears everything up.

[QUOTE=kar_bon]BTW: k=337 got no prime for 172000<n<2600000!
[/QUOTE]

Perform a k-range search. Constant probability is awesome.

Now, to wait for sm88 to explain the unspecified sequences.

Some sample numbers:
[CODE]Base|Exponent|Prob.|#tests |K Range |Cand Left|Sieve |#tests |
| |Boost|(before)|(3*#tests)|(p=10^12)|efficiency|(after)|
----+--------+-----+--------+----------+---------+----------+-------|
2 | 250000| 2| 86643 | 259929 | 10563 | 24.61 | 3520 |
6 | 96713| 3| 57762 | 173286 | 10563 | 16.40 | 3522 |
30 | 50948| 3.75| 46209 | 138627 | 10563 | 13.12 | 3522 |
210 | 32407|4.375| 39607 | 118821 | 10563 | 11.25 | 3520 |
[/CODE]

[QUOTE=3.14159;224026]Ah, I see what the problem is: You assumed I did n-range searches. I perform k-range searches, which means I search for primes in arithmetic progressions.

Maybe this clears everything up.



Perform a k-range search. Constant probability is awesome.

Now, to wait for sm88 to explain the unspecified sequences.[/QUOTE]

look m for 24m+7 takes on values that appear in sequence related to p all I was trying to do is find a way to use these to sieve out of the sequences involved with the sequence in the OEIS i posted a link to earlier.

85 Mod 23 = 16 the start c

16*4+1 = 65-23 = 42 then -23 = 19
19*4+1 = 77-23 = 54-23 again = 31 - 23 again = 8
8*4+1 = 33-23=10
10*4+1 = 41 - 23=18
18*4+1=73 - 23 = 50 -23=27-23 =4
4*4+1 = 17
17*4+1 = 69 -23 = 46-23=23-23=0

@Axn: The data explains it all. Inefficient sieving is why I stick to factor-deficient or prime bases.

[QUOTE=3.14159;224032]@Axn: The data explains it all. Inefficient sieving is why I stick to factor-deficient or prime bases.[/QUOTE]

If that is the conclusion, you've not understood that table at all.

See the columns K-Range, Cands Left, # tests (before) and # tests (after). Those are the key thing. If the sieve efficiency is less for a factor rich base, it compensates it (exactly) by allowing a smaller starting k-range. The net effect is that you _test_ the same number of candidates after sieving. The expected number of tests (~3520) for finding a prime is the same for everything, _after_ sieving.

Right. axn, thanks for explaining; you do it better than I can.

[QUOTE=axn]See the columns K-Range, Cands Left, # tests (before) and # tests (after). Those are the key thing. If the sieve efficiency is less for a factor rich base, it compensates it (exactly) by allowing a smaller starting k-range. The net effect is that you _test_ the same number of candidates after sieving. The expected number of tests (~3520) for finding a prime is the same for everything, _after_ sieving.
[/QUOTE]

Ah, okay. I didn't notice that before. But it ultimately shows that factor-deficient/prime bases are more efficient than factor-rich bases.

[QUOTE=CRGreathouse]Right. axn, thanks for explaining; you do it better than I can.
[/QUOTE]

[B]And since when does this warrant a license for implicit insults?[/B]

[QUOTE=3.14159;224039][B]And since when does this warrant a license for implicit insults?[/B][/QUOTE]

I think, conversationally speaking, I'm allowed to self-deprecate. It's difficult for me to understand others (so I asked, e.g., you to explain sm88's posts), and similarly hard for me to be understood (so axn's explanation worked when mine didn't).

Also: About the Prime Pages' database: Can one register to have a prime listed in the misc. primes in their database (Primes that are special-form, but do not make it to the top 5k.)

Here's an example: 3 * 2[sup]213321[/sup] + 1 is present, but it does not register for the top 5k, but is stored there because it is a prime Proth number.

[QUOTE=3.14159;224039]But it ultimately shows that factor-deficient/prime bases are more efficient than factor-rich bases.[/QUOTE]

You'll have to explain your reasoning.

[QUOTE=axn]You'll have to explain your reasoning.[/QUOTE]

You were forced to lower the k-range when dealing with factor-rich numbers in order to get the same amount of candidates. The data there verifies this. Which means factor-rich bases leave too many candidates and waste time on obvious composites that could have been eliminated, and as a result are a terrible choice for prime searching.

If you would have kept the k-range constant, it would further prove the inefficiency of using a factor-rich base.