To find first N prime numbers in python

Question

I am new to the programming world  I was just writing this code in python to generate N prime numbers  User should input the value for N which is the total number of prime numbers to print out  I have written this code but it doesn t throw the desired output  Instead it prints the prime numbers till the Nth number  For example  User enters the value of N   7  Desired output  2  3  5  7  11  13  19 Actual output  2  3  5  7 Kindly advise  i   1 x   int input  quot Enter the number  quot    for k in range 1  x 1       c   0     for j in range 1  i 1           a   i   j         if a    0              c   c   1      if c    2          print i      else          k   k - 1      i   i   1

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I am not familiar with Python so I am writing the C counter part too lazy to write pseudo code    P  To find the first n prime numbers       prints all the primes   not bothering to make an array and return it etc    void find first n primes int n      int count   0     for int i 2 count lt  n i          factFlag    0    flag for factor count          for int k 2 k lt sqrt n  1 k            if i k    0     factor found           factFlag                 if factFlag  0    no factors found hence prime                      Print i        prime displayed            count

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def isprime n       if n  lt   1          return False     for x in range 2  n           if n   x    0              return False     else          return True  def list prime z       y   0     def to infinity            index 0         while 1              yield index             index    1     for n in to infinity            if y  lt  z              if isprime n                   y   y   1                 print n  end   n   flush True          else break     print f  n  z  prime numbers are as above       put your range below list prime 10

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Here s a simple recursive version   import datetime import math  def is prime n  div 2       if div gt  int math sqrt n    return True     if n  div    0          return False     else          div  1         return is prime n div    now   datetime datetime now    until   raw input  How many prime numbers my lord desires       until   int until   primelist    i 1  while len primelist  lt until      if is prime i           primelist insert 0 i          i  1     else  i  1    print                        print primelist finish   datetime datetime now   print  It took your computer   finish - now    secs to calculate it    Here s a version using a recursive function with memory    import datetime import math  def is prime n  div 2       global primelist     if div gt  int math sqrt n    return True     if div  lt  primelist 0           div   primelist 0          for x in primelist              if x   0 or x  1  continue             if n   x    0                  return False     if n  div    0          return False     else          div  1         return is prime n div    now   datetime datetime now   print  time and date   now  until   raw input  How many prime numbers my lord desires       until   int until   primelist    i 1  while len primelist  lt until      if is prime i           primelist insert 0 i          i  1     else  i  1    print  Here you go   print primelist  finish   datetime datetime now   print  It took your computer   finish - now     to calculate it    Hope it helps

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using a regexp        usr bin python  import re  sys   def isPrime n         see http   www noulakaz net weblog 2007 03 18 a-regular-expression-to-check-for-prime-numbers      return re match r  1     11    1      1    n     None   N   int sys argv 1     number of primes wanted  from command-line  M   100                upper-bound of search space l   list               result list  while len l   lt  N      l    filter isPrime  range M - 100  M     append prime element of  M - 100  M  to l     M    100                                  increment upper-bound  print l  N    print result list limited to N elements

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Hi  I am very new to coding  just started 4 days back  I wrote a code to give back the first 1000 prime numbers including 1  Have a look n 1 c 0 while n gt 0     for i in range 2 n         if n i    0           break    else        print n  is a prime         c c 1    n n 1    if c  1000        break

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usr bin python3 import sys  primary numbers    1  2    def is prime i       for pn in enumerate primary numbers 2             if i   pn 1     0              return False      return True  def main position       i   3     while len primary numbers   lt  int position           print i          res   is prime i          if res              primary numbers append i          i    2   if   name         main         position   sys argv 1      main position      print primary numbers

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def isPrime y     i 2   while i  lt  y      if y i    0         return 0       exit       i i 1   return 1  x  raw input  Enter the position 1st 2nd   nth prime number you are looking for      z int x    for l in range 2 z  count   1 n   2 while count  lt   z    if isPrime n     1      if count    z        print n     count   1   n n 1

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count   -1 n   int raw input  how many primes you want starting from 2     primes      n for p in range 2  n  2       for i in range 2  p           if p   i    0              break     else          count   1         primes count   p         if count    n-1              break  print  primes  print  Done

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def Isprime z          returns True if the number is prime OTW returns false        if z lt 1          return False     elif z  1          return False      elif z  2          return True       else          for i in range 2 z               if z i  0                  return False             else                  return True   This is the way I did it  Of course  there are so many ways you can do it

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Super quick sieve implementation by David Eppstein - takes 0 146s for the first 1000 primes on my PC   def gen primes            Generate an infinite sequence of prime numbers                Maps composites to primes witnessing their compositeness        This is memory efficient  as the sieve is not  run forward        indefinitely  but only as long as required by the current       number being tested            D               The running integer that s checked for primeness     q   2        while True          if q not in D                q is a new prime                Yield it and mark its first multiple that isn t               already marked in previous iterations                            yield q                     D q   q     q          else                q is composite  D q  is the list of primes that               divide it  Since we ve reached q  we no longer               need it in the map  but we ll mark the next                multiples of its witnesses to prepare for larger               numbers                            for p in D q                   D setdefault p   q      append p              del D q           q    1  primes   gen primes     x   set   y   0 a   gen primes   while y  lt  10000    x    set  a next       y  1  print  x contains    d  primes  format len x   print  largest is    d   format sorted x  -1

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This is my version  import timeit import math    author      rain    primes    2   def is prime n       for prime in primes          if n   prime    0              return False     return True   def find nth prime n       current index   0     while len primes   lt  n           if current index    0              start value   3             end value   2   2         else              start value   primes current index - 1    primes current index - 1    1             end value   primes current index    primes current index          for i in range start value  end value               if is prime i                   primes append i          current index    1     return primes n-1    def solve        return find nth prime 10001   print solve    print timeit timeit solve  number 10    I use a sieve to scan primes  it s quite quick  It s take only 3 8e-06 seconds to get 10001th prime  10 times

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For reference  there s a pretty significant speed difference between the various stated solutions  Here is some comparison code  The solution pointed to by Lennart is called  historic   the one proposed by Ants is called  naive   and the one by RC is called  regexp    from sys import argv from time import time  def prime i  primes       for prime in primes          if not  i    prime or i   prime               return False     primes add i      return i  def historic n       primes   set  2       i  p   2  0     while True          if prime i  primes               p    1             if p    n                  return primes         i    1  def naive n       from itertools import count  islice     primes    n for n in count 2  if all n   d for d in range 2  n        return islice primes  0  n   def isPrime n       import re       see http   tinyurl com 3dbhjv     return re match r  1     11    1      1    n     None  def regexp n       import sys     N   int sys argv 1     number of primes wanted  from command-line      M   100                upper-bound of search space     l   list               result list      while len l   lt  N          l    filter isPrime  range M - 100  M     append prime element of  M - 100  M  to l         M    100                                  increment upper-bound      return l  N    print result list limited to N elements  def dotime func  n       print func   name       start   time       print sorted list func n        print  Time in seconds      str time   - start   if   name         main         for func in naive  historic  regexp          dotime func  int argv 1      The output of this on my machine for n   100 is   naive  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  Time in seconds  0 0219371318817 historic  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  Time in seconds  0 00515413284302 regexp  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  Time in seconds  0 0733318328857   As you can see  there s a pretty big discrepancy  Here it is again for 1000  prime outputs removed    naive Time in seconds  1 49018788338 historic Time in seconds  0 148319005966 regexp Time in seconds  29 2350409031

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Using generator expressions to create a sequence of all primes and slice the 100th out of that   from itertools import count  islice primes    n for n in count 2  if all n   d for d in range 2  n    print  100th prime is  d    next islice primes  99  100

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n int input  Enter the number        for i in range 2 n       p i     k 0     for j in range 2 p-1           if p j  0               k k 1     if k  0           print p

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This code is very confused  and I can t figure out exactly what you were thinking when you wrote it or what you were attempting to accomplish   The first thing I would suggest when trying to figure out how to code is to start by making your variable names extremely descriptive   This will help you get the ideas of what you re doing straight in your head  and it will also help anyone who s trying to help you show you how to get your ideas straight   That being said  here is a sample program that accomplishes something close to the goal   primewanted   int input  This program will give you the nth prime  nPlease enter n     if primewanted  lt   0      print  n must be  gt   1  else      lastprime   2   2 is the very first prime number     primesfound   1    Since 2 is the very first prime  we ve found 1 prime     possibleprime   lastprime   1   Start search for new primes right after     while primesfound  lt  primewanted            Start at 2   Things divisible by 1 might still be prime         testdivisor   2           Something is still possibly prime if it divided with a remainder          still possibly prime     possibleprime   testdivisor     0             testdivisor   1  because we never want to divide a number by itself          while still possibly prime and   testdivisor   1   lt  possibleprime               testdivisor   testdivisor   1             still possibly prime     possibleprime   testdivisor     0            If after all that looping the prime is still possibly prime            then it is prime          if still possibly prime              lastprime   possibleprime             primesfound   primesfound   1           Go on ahead to see if the next number is prime         possibleprime   possibleprime   1     print  This nth prime is    lastprime   This bit of code           testdivisor   2           Something is still possibly prime if it divided with a remainder          still possibly prime     possibleprime   testdivisor     0             testdivisor   1  because we never want to divide a number by itself          while still possibly prime and   testdivisor   1   lt  possibleprime               testdivisor   testdivisor   1             still possibly prime     possibleprime   testdivisor     0    could possibly be replaced by the somewhat slow  but possibly more understandable             Assume the number is prime until we prove otherwise         still possibly prime   True           Start at 2   Things divisible by 1 might still be prime         for testdivisor in xrange 2  possibleprime  1                 Something is still possibly prime if it divided with a               remainder   And if it is ever found to be not prime  it s not               prime  so never check again              if still possibly prime                  still possibly prime     possibleprime   testdivisor     0

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Try using while loop to check the count  that is easy  Find the code snippet below    i 1 count   0  x   int input  Enter the number  n    while  count  lt  x   c 0 for j in range  1   i 1   1       a   i j     if  a  0           c   c 1  if  c  2         print  i        count   count 1 i i 1

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Here s what I eventually came up with to print the first n primes   numprimes   raw input  How many primes to print      count   0 potentialprime   2  def primetest potentialprime       divisor   2     while divisor  lt   potentialprime          if potentialprime    2              return True         elif potentialprime   divisor    0              return False             break         while potentialprime   divisor    0              if potentialprime - divisor  gt  1                  divisor    1             else                  return True  while count  lt  int numprimes       if primetest potentialprime     True          print  Prime      str count   1    is   potentialprime         count    1         potentialprime    1     else          potentialprime    1

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You can take the number of prime number inputs  As per your method I have taken here a predefined count of 10    i   2 if i    2      print str i     is a prime no       i   i 1 c 1  while c lt 10      for j in range 2  i           if i j  0              break      if i    j 1          print str i     is aa prime no           c c 1      i i 1

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Fastests import math  n   10000  first 10000 primes tmp n   1 p   3  primes    2    while tmp n  lt  n       is prime   True      for i in range 3  int math sqrt p    1   2             range with step 2          if p   i    0              is prime   False      if is prime          primes     p          tmp n    1      p    2  print primes

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This might help   import sys from time import time def prime N       M 100     l        while len l   lt  N          for i in range M-100 M                   num   filter lambda y  i   y    0  y for y in range 2   i 2                  if not num and i not in  0 1 4                   l append i          M   100     return l  N    def dotime func  n       print func   name       start   time       print sorted list func n    len list func n        print  Time in seconds      str time   - start    if   name         main         dotime prime  int sys argv 1

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Anwer here is simple i e run the loop  n  times   n int input    count 0 i 2 while count lt n      flag 0     j 2     while j lt  int i  0 5           if i j  0              flag  1         j  1     if flag  0          print i end              count  1     i  1

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prime 2 counter   0 x   int input  Enter the number  n    while  counter  lt  x       if all prime j  0 for j in range 2  prime            print prime   is a prime number           counter  1       prime  1

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Try this   primeList      for num in range 2 10000       if all num i  0 for i in range 2 num            primeList append num  x   int raw input  Enter n      for i in range x       print primeList i

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The line k   k-1 does not do what you think  It has no effect  Changing k does not affect the loop  At each iteration  k is assigned to the next element of the range  so any changes you have made to k inside the loop will be overwritten

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Until we have N primes  take natural numbers one by one  check whether any of the so-far-collected-primes divide it    If none does   yay   we have a new prime      that s it    gt  gt  gt  def generate n primes N           primes               chkthis   2         while len primes   lt  N              ptest       chkthis for i in primes if chkthis i    0              primes        if ptest else  chkthis              chkthis    1         return primes      gt  gt  gt  print generate n primes 15   2  3  5  7  11  13  17  19  23  29  31  37  41  43  47

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max   input  enter the maximum limit to check prime number    if max gt 1       for i in range  2 max           prime 0          for j in range  2 i               if i j  0                   prime 1                  break         if prime  0 and i  0               print i  is prime number    else      print  prime no start from 2

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This might help   def in prime n       p True     i 2     if i  2 lt  n          if n i  0              p False             break     if  p           return n

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What you want is something like this  x   int input  quot Enter the number  quot    count   0 num   2 while count  lt  x       if isnumprime x           print x          count    1      num    1  I ll leave it up to you to implement isnumprime      Hint  You only need to test division with all previously found prime numbers

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Whilst playing with prime numbers in Python V3 I noticed that the smallest number by which a composite non-prime  number is divisible is itself always a prime that is less than the square root of the number under test   Below is my implementation of that finding to calculate the first N prime numbers   first 1 000 primes in 0 028S     first 10 000 primes in 0 6S     first 100 000 primes in 14 3S  The snippet below also indicates how long the generation took and prints out the primes in a nice table format   import time import math  def first n Primes n       number under test   4     primes    2 3      while len primes   lt  n          check   False         for prime in primes              if prime  gt  math sqrt number under test    break             if number under test   prime    0                  check   True                 break         if not check              for counter in range primes len primes -1  number under test-1 2                   if number under test   counter    0                      check   True                     break         if not check              primes append number under test          number under test  1     return primes  start time   time time   data   first n Primes 1000  end time   time time    i   1 while i  lt  len data  1      print   0   lt 9   format str data i-1     end         if i 10    0  print         i  1  print   nFirst  d primes took  s seconds ---     len data  end time - start time

[python] To find first N prime numbers in python

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