Ë
    óÿæiM
  ã                   óF   — d dl mZ d„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd	„ Z	d
„ Z
y)é    )Úsqrtc                  ó´   — t        d«       t        d«       t        d«       t        d«       t        d«       t        d«       t        d«       t        d«       y )	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    úc/Volumes/fast/ai/experiments/voice-extract-mac/.venv/lib/python3.12/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                 óˆ   — | dk(  s| dz  dk(  ryt        dt        t        | «      «      dz   d«      D ]  }| |z  dk(  sŒ|c S  | S )Né   r   é   é   )ÚrangeÚintr   )ÚnumÚis     r   Úfactorr      sM   € Ø
ˆA‚v��Q‘˜’Øä�qœ#œd 3›i›.¨Ñ*¨AÖ.ˆAØ�1‰u�a‹xØ’ð /ð ˆJr   c                 ó"   — t        | «      | k(  ryy)NTF©r   )r   s    r   Úcheckr      s   € Üˆcƒ{�CÒØàr   c                 ón   — t        | «      }| |z  }|g}|dk7  rt        |«      }||gz  }||z  }|dk7  rŒ|S ©Nr   r   )r   ÚfactÚnew_numÚfactorss       r   r   r   #   sO   € Ü	�‹€DØ�‰I€GØˆF€GØ
�1Š*Ü�G‹_ˆØ�$�‰ˆØ�$‰ˆð �1‹*ð €Nr   c                 óZ   — | }t        | «      }t        |«      }|D ]  }||z  |dz
  z  }Œ |S r   )r   Úset)r   ÚvalÚlistÚsetsr   s        r   Úphir    -   s9   € Ø€CÜ	�‹€DÜ	ˆT‹€DÛˆØ�!‰V�a˜‘c‰N‰ð à€Jr   c                 ót   — | dgk(  rd}|S | d   dz   }d}|dk(  r| D ]  }||z  dk(  sŒ|dz   } n d}|dk(  rŒ|S )Nr   r   éÿÿÿÿr   r   r   )r   ÚaÚfoundr   s       r   Ú__next_primer%   6   sj   € ØˆaˆS‚yØ
ˆð €Hð ˆr‰(�1‰*ˆØˆØ�QŠhÛ�Ø�Q‘3˜“6Ø˜‘c�AÙð ð
 �ð �Q‹hð €Hr   c                 óh   — dg}t        |«      | k  r t        |«      }||gz  }t        |«      | k  rŒ |S )Nr   )Úlenr%   ©Únr   Ú	new_entrys      r   Úfirstr+   F   s>   € Ø
ˆ€DÜ
ˆd‹)�AŠ+Ü˜tÓ$ˆ	ØˆyˆkÑˆô ˆd‹)�A‹+ð €Kr   c                 ój   — dg}|d   | k  rt        |«      }||gz  }|d   | k  rŒ|d   | kD  r|d d }|S )Nr   r"   )r%   r(   s      r   Úuptor-   M   sT   € Ø
ˆ€DØ
ˆr‰(�1Š*Ü˜tÓ$ˆ	ØˆyˆkÑˆð ˆr‰(�1‹*ð ˆB�x�‚zØ�#�2ˆYˆØ€Kr   c                 óz   — d}g }| dz  dk(  rd}nd}t        | |z   |d«      D ]  }t        |«      r||gz  }Œ|}Œ |S )Nr   r   r   )r   r   )Úmr)   ÚdÚxr   s        r   Úbetweenr2   V   sU   € Ø€AØ€AØˆ�sˆA‚vØ
‰à
ˆÜ�1�Q‘3�q˜Ž^ˆÜ�Œ8Ø�ˆs‰F‰Aà‰Að	 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   