Example prime numbers

[krzysztof]

Very simple program for calculation of prime numbers:

'Program determines the prime numbers using the method of checking divisibility
cls
input "Enter limit"; n
for p = 2 to n
 'Instead of (p - 1) one can use sqr(p) for faster calculations
 for q = 2 to p - 1
  'Instead of 
 onecan use (p mod q = 0)
  if p / q = int(p / q) then goto [nextp]
 next q
 print p; " ";
[nextp]
next p
end

[krzysztof]

...And its small modification. Rejected numbers are saved as dots.

'Program determines the prime numbers using the method of checking divisibility
'The rejected numbers are recorded as dots
cls

input "Enter limit"; n

for p = 2 to n
 'Instead of (p - 1) one can use sqr(p) for faster calculations
 for q = 2 to p - 1
  'Instead of 
 one can use (p mod q = 0)
  if p / q = int(p / q) then goto [dot]
 next q

 print p;
 goto [nextp]

 [dot]
 print ".";
[nextp]
next p

end

The numbers and dots are written in a single line, but it's worth look the version called Ulam spiral en.wikipedia.org/wiki/Ulam_spiral. The resulting gaps between the numbers are arranged in an interesting pattern.

[krzysztof]

At the begining of the second page of "Run BASIC – A Breakthrough Web Application Server" document www.libertybasic.com/RunBASICBreakthrough.pdf there is an example of code for estimating time of prime numbers's calculation. It can display primes if we insert a command print prime inside if-then loop. But it is not a sieve of Eratostenes. Do You know what is the name ot that algorithm?