ó
    ‰“,jM
  ã                   óF   • S SK Jr  S rS rS rS rS rS rS rS	 r	S
 r
g)é    )Úsqrtc                  ó´   • [        S5        [        S5        [        S5        [        S5        [        S5        [        S5        [        S5        [        S5        g )	Nz9'primes.check(n)' returns 'True' if 'n' is a prime numberz9'primes.factor(n)' returns the lowest prime factor of 'n'zI'primes.facors(n)' returns all the prime factors of 'n' with multiplicityz/'primes.first(n)' returns first 'n' many primeszA'primes.upto(n)' returns all the primes less than or equal to 'n'z@'primes.between(m,n)' returns all the primes between 'm' and 'n'z*'primes.phi(n)' returns the Euler's phi(n)zDi.e., the number of integers less than n which have no common factor)Úprint© ó    ÚœC:\Users\johnn\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.13_qbz5n2kfra8p0\LocalCache\local-packages\Python313\site-packages\primePy/primes.pyÚaboutr	      sJ   € Ü	Ð
KÔLÜ	Ð
IÔJÜ	Ð
YÔZÜ	Ð
?Ô@Ü	Ð
QÔRÜ	Ð
RÔSÜ	Ð
8Ô9Ü	Ð
PÕQr   c                 ó�   • U S:X  d	  U S-  S:X  a  g[        S[        [        U 5      5      S-   S5       H  nX-  S:X  d  M  Us  $    U $ )Né   r   é   é   )ÚrangeÚintr   )ÚnumÚis     r   Úfactorr      sK   € Ø
ˆAƒv��Q‘˜“Øä�qœ#œd 3›i›.¨Ñ*¨AÖ.ˆAØ‰u�a�xØ’ñ /ð ˆJr   c                 ó$   • [        U 5      U :X  a  gg)NTF©r   )r   s    r   Úcheckr      s   € Üˆcƒ{�CÓØàr   c                 ón   • [        U 5      nX-  nU/nUS:w  a  [        U5      nX1/-  nX!-  nUS:w  a  M  U$ ©Nr   r   )r   ÚfactÚnew_numÚfactorss       r   r   r   #   sI   € Ü	�‹€DØ‰I€GØˆF€GØ
�1‹*Ü�G‹_ˆØ�‰ˆØ‰ˆð �1�*ð €Nr   c                 ó\   • U n[        U 5      n[        U5      nU H  nX-  US-
  -  nM     U$ r   )r   Úset)r   ÚvalÚlistÚsetsr   s        r   Úphir    -   s7   € Ø€CÜ	�‹€DÜ	ˆT‹€DÛˆØ‰V�a˜‘c‰NŠñ à€Jr   c                 ó€   • U S/:X  a  SnU$ U S   S-   nSnUS:X  a"  U  H  nX-  S:X  d  M  US-   n  O   SnUS:X  a  M"  U$ )Nr   r   éÿÿÿÿr   r   r   )r   ÚaÚfoundr   s       r   Ú__next_primer%   6   sh   € ØˆaˆSƒyØ
ˆð €Hð ˆr‰(�1‰*ˆØˆØ�Q‹hÛ�Ø‘3˜•6Ø˜‘c�AÙñ ð
 �ð �Q�hð €Hr   c                 ól   • S/n[        U5      U :  a!  [        U5      nX/-  n[        U5      U :  a  M!  U$ )Nr   )Úlenr%   ©Únr   Ú	new_entrys      r   Úfirstr+   F   s<   € Ø
ˆ€DÜ
ˆd‹)�A‹+Ü˜tÓ$ˆ	ØˆkÑˆô ˆd‹)�A�+ð €Kr   c                 óp   • S/nUS   U :  a  [        U5      nX/-  nUS   U :  a  M  US   U :”  a  US S nU$ )Nr   r"   )r%   r(   s      r   Úuptor-   M   sR   € Ø
ˆ€DØ
ˆr‰(�1‹*Ü˜tÓ$ˆ	ØˆkÑˆð ˆr‰(�1�*ð ˆB�x�ƒzØ�#�2ˆYˆØ€Kr   c                 óˆ   • Sn/ nU S-  S:X  a  SnOSn[        X-   US5       H  n[        U5      (       a  X4/-  nM  UnM     U$ )Nr   r   r   )r   r   )Úmr)   ÚdÚxr   s        r   Úbetweenr2   V   sS   € Ø€AØ€AØˆ�sˆAƒvØ
‰à
ˆÜ�1‘3�q˜Ž^ˆÜ��8‰8Øˆs‰FŠAàŠAñ	 ð
 €Hr   N)Úmathr   r	   r   r   r   r    r%   r+   r-   r2   r   r   r   Ú<module>r4      s8   ðõ òRòòòòòò òór   