Thread: Double checking
View Single Post
Old 2007-08-25, 23:30   #8
gd_barnes
 
gd_barnes's Avatar
 
May 2007
Kansas; USA

244328 Posts
Default Problems for k=250-1001 to n=25K and some others

I have completed double-checking the entire range of 250 < k <= 1001 for n <= 25K as well as some other misc. double-checks. I found the following problems for k=250-1001.

Missing primes:
315*2^21970-1
321*2^18053-1
325*2^24707-1
373*2^19027-1
673*2^19447-1
859*2^16437-1
859*2^23759-1

Incorrect primes:
431*2^1543-1 should be 431*2^1542-1
651*2^24035-1 should be 651*2^24025-1

Composite that needs to be removed:
945*2^21062-1 (has a factor of 1,106,129)

I also noticed 6 k's that had unusually large gaps between their primes for their specific weight. They are k=307, 341, 509, 543, 599, and 737. I tested k=307 and 341 up to n=100K. In doing this, I found 2 more missing primes.

Missing primes:
341*2^72814-1
341*2^86418-1

I have also double-checked 14 of the 16 k's that I currently have reserved up to n=150K for primes that were previously found by others. (I didn't double-check any of my own work on my reserved k's.) I found two problems on one of the k's.

Missing prime:
16995*2^79110-1

Incorrect prime:
16995*2^81429-1 should be 16995*2^81439-1


When I found missing and incorrect primes, I double-checked my own work, which means that the above primes are now effectively triple-checked!

Analysis: There were no missing primes and only one error on primes from the Prime Search site below n=16K but many problems from n=16K to 25K. I saw that the range of n=0 to 16K was never set up as a reserved range on the site. Therefore, I suspect that the primes were previously calculated elsewhere -or- were calculated ahead of time before the site was ever set up and then were copied over there -or- were calculated there but were double or even triple-checked. To be that extremely accurate below n=16K and highly inaccurate from n=16K to 25K is very unusual. What makes it more unusual is that there may be 100 times or more as many primes from n=1 to 16K as there are from 16K to 25K.

Status on upcoming double-check work in the next post...


Gary
gd_barnes is offline   Reply With Quote