In[24]:=
SieveOfEratosthenes[n_]:=
Module[ {t,P,i=1,x},
t=N[Sqrt[n]];
P=Range[2,n];
While[ P[[i]] <= t,
x=Table[k P[[i]],
{k,P[[i]], Floor[n/P[[i]]]}];
P=Complement[P,x];
i++];
Return[P]]
In[25]:=
SieveOfEratosthenes[100]
Out[25]=
{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}
Remarks: Do not use this sieve to generate primes for n more than 10^5 as it
is
likely to be very slow. For larger n, it is better to modify the sieve to
generate
primes between n1 and n2, by reading in a list of primes up to square root of
n2.
Also, it is better to save the result in a file rather than display it on a
screen. This
can be done by the >> operator and the file can be read in using
<< or the
ReadList command.
In[26]:=
SieveOfEratosthenes[ 1000]>> primes;
In[27]:=
primes= ReadList[ "primes", Expression];
In[28]:=
primes
Out[28]=
{{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997}}
Notice the extra set of braces around the expression. These can be removed
using the Flatten command.
In[29]:=
primes=Flatten[primes];
primes[[50]]
Out[29]=
229
Exercise: Write a function Sieve[n,m] to create a list of primes between n and
m. To start
the sieve you will need a list of primes up to square root of m.
Up to Procedural Programming