Statistics on primes

[daydreamer]

Hi
I am probably not the only one who like statistics and curves
After looking at list with loads of primes
Would be interesting create statistics for last digits is of number is a prime

[raymond]

Only the terminating digits 1, 3, 7 and 9 can be considered for prime numbers (the only exceptions being the actual prime numbers 2 and 5).

If your sample is large enough, each of those four terminating digits would likely be close to 25%.

[daydreamer]

Only the terminating digits 1, 3, 7 and 9 can be considered for prime numbers (the only exceptions being the actual prime numbers 2 and 5).

If your sample is large enough, each of those four terminating digits would likely be close to 25%.

Very big primes BCD it saves lot of CPU cycles with determine ending with even number and '5' using
 test al,1 and cmp al,'5' faster than idiv 5
Or keyboard input string ,process last digit can skip even conversion to integer and rest of prime testing


Take a look at some of two last digits are the same
1   2   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17   18   19   20
1–20   2   3   5   7   11   13   17   19   23   29   31   37   41   43   47   53   59   61   67   71
21–40   73   79   83   89   97   101   103   107   109   113   127   131   137   139   149   151   157   163   167   173
41–60   179   181   191   193   197   199   211   223   227   229   233   239   241   251   257   263   269   271   277   281
61–80   283   293   307   311   313   317   331   337   347   349   353   359   367   373   379   383   389   397   401   409
81–100   419   421   431   433   439   443   449   457   461   463   467   479   487   491   499   503   509   521   523   541
101–120   547   557   563   569   571   577   587   593   599   601   607   613   617   619   631   641   643   647   653   659
121–140   661   673   677   683   691   701   709   719   727   733   739   743   751   757   761   769   773   787   797   809

[zedd151]

Would be interesting create statistics for last digits is of number is a prime

Only the terminating digits 1, 3, 7 and 9 can be considered for prime numbers (the only exceptions being the actual prime numbers 2 and 5).
If your sample is large enough, each of those four terminating digits would likely be close to 25%.

A small test... to count each occurence of the last digit in a set of prime numbers for daydreamer. The code was adapted to tally the last digit in each prime number, and is very untidy - apologies.  but it does seem to do what you were looking for. You can add code Magnus, to get the exact floating point percentages. 

Code Select Expand

Total Primes = 46009215
Primes from 0 until 900000000

0's = 0
1's = 11502079
2's = 1
3's = 11502577
4's = 0
5's = 1
6's = 0
7's = 11502549
8's = 0
9's = 11502008


What I find more interesting about prime numbers daydreamer, are the prime numbers that are exactly 2 apart from another prime number (i.e., 101 and 103). There is a name for those, but it escapes me at the moment...

Later: I looked it up, they are called Twin Primes. 

[daydreamer]

thanks Zedd 

[zedd151]

thanks Zedd 

Not a problem.
The results are pretty much as Raymond suggested above, that they should be. The more prime numbers that are tested, the closer the results will be to 25% of the total of all the prime numbers within a given range.

[daydreamer]

so using a tiny circular buffer containing 1,3,7,9 when prime testing loop from 10 upto desireed range you only need test 40% of numbers
 
my 0-65535 prime LUT ,ca 10% of the numbers in this range are primes
I was thinking output primes write to 1 bit BMP ,but this gif on this page shows it best when you want to image to better understand where primes are
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes