20100407, 00:34  #34 
"Ben"
Feb 2007
CDA_{16} Posts 

20100407, 00:48  #35  
Jun 2003
7·11·61 Posts 
Quote:
Code:
p=2;s=0;ten=10;for(i=2,10000000,s=s+p;if(Mod(s,ten)==0, ten=ten*10;print(i,":",p, ":",s)); p=nextprime(p+1)) 4:5:10 10:23:100 3796:35677:63731000 10184:106853:515530000 51532:632501:15570900000 1926966:31190879:29057028000000 3471032:58369153:98078160000000 

20100407, 01:01  #36 
Jun 2003
7×11×61 Posts 
While we're at it, some results for the cubes:
Code:
3:5:160 51:233:143309500 1095:8783:167992435025000 2739:24763:9495929161130000 401785:5828099:18803849605481106073200000 616801:9229931:114943299218925309364000000 14335805:262707241:62239590622437034770047320000000 
20100407, 03:40  #37 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
4387_{10} Posts 

20100407, 04:46  #38  
"Ben"
Feb 2007
2·5·7·47 Posts 
Quote:
Code:
**** 10 divides prime cube sum up to 5, sum = 160 **** **** 100 divides prime cube sum up to 233, sum = 143309500 **** **** 1000 divides prime cube sum up to 8783, sum = 167992435025000 **** **** 10000 divides prime cube sum up to 24763, sum = 9495929161130000 **** **** 100000 divides prime cube sum up to 5828099, sum = 18803849605481106073200000 **** **** 1000000 divides prime cube sum up to 9229931, sum = 114943299218925309364000000 **** **** 10000000 divides prime cube sum up to 262707241, sum = 62239590622437034770047320000000 **** **** 100000000 divides prime cube sum up to 7717488553, sum is 39389391603365585735745579849700000000 **** **** 1000000000 divides prime cube sum up to 34529828929, sum = 14800565770732540706707662233175000000000 **** **** 10000000000 divides prime cube sum up to 311995561321, sum = 90365528187658782254536155073531290000000000 **** 

20100407, 14:08  #39  
"Ben"
Feb 2007
CDA_{16} Posts 
Quote:
Code:
**** 100000000000 divides prime cube sum up to 549120448879, sum is 848814744633978332442418792098769600000000000 **** 

20100407, 14:17  #40  
"Ben"
Feb 2007
2×5×7×47 Posts 
Quote:
A single 64 bit integer runs out of precision at about 1.8e19, which is enough for the prime sum up to about 9 billion. Since you found the point at (632501 15570900000), you must be using more than 32 bits... but with 64 bits you should be fine for a few more points of the sequence. So maybe its an issue with your prime generation as well. A useful double check is to see if the count of primes you've summed agrees with known prime counts. For instance here. Last fiddled with by bsquared on 20100407 at 14:18 

20100407, 17:34  #41 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
41×107 Posts 
YUP precision.

20100408, 14:28  #42 
May 2004
New York City
2×3^{2}×5×47 Posts 
Another way to extend this problem is to use
a base other than ten. I think binary. 2^2 + 3^2 + 5^2 + ... + p^2 = 2^{m}K What is the smallest prime p such that the sum of squares of all primes up to p is a multiple of 2 (or 4 or 8 or 16 or ...). This question can also be asked of first powers or cubes of primes. Since we basically compute in decimal or binary, if there's an interesting number theoretic fact here we may find it in one of these two related sequences of sequences. 
20100408, 14:55  #43 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 

20100410, 01:35  #44  
Mar 2010
Brick, NJ
67 Posts 
Quote:
1 907 37464550 2 977 46403000 3 977 46403000 You have duplicated 2 and 3 on your site. I also noted that the OEIS sequence didn't have example code. Perhaps you could submit the expression you have entered into YAFU. Last fiddled with by alexhiggins732 on 20100410 at 01:35 Reason: Table HTML was stripped... 

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