python program about fields of primes

field.py

# python program about fields of primes

def divnr(a,b): # a/b , div.ide n.on r.repeating
    la=[]
    string=''
    psum=0
    idx=-1
    while True:
        a*=10
        # if a in la: break
        try:
            idx=la.index(a)
            break
        except ValueError:
            pass
        la+=[a]
        c=a//b
        d=a%b
        string+=str(c)
        psum+=c; psum%=9
        a=d
    return idx,psum,len(string),string

def field(n):
    for i in range(1,n):
        # print(i/n)
        print(divnr(i,n))

prime_table=[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]

def fields(prime_table):
    for n in prime_table:
        field(n)

def is_prime(n):
    length_a=-1
    for i in range(1,n):
        idx, psum, length_b, string=divnr(i,n)
        if length_a!=length_b:
            if length_a==-1: length_a=length_b
            else: return False
        if psum!=0: return False
        if idx!=0: return False
    return True

def is_prime_simple(n):
    for i in range(2,n):
        if n%i==0: return False
    return n not in (2,3,5)

def calc_primes(max):
    primes=[]
    for n in range(2,max+1):
        if is_prime(n): primes+=[n]
    return primes

if __name__=='__main__':
    # fields(prime_table)

    print('field of 91:')
    field(91)
    
    print('is 91 prime? ', is_prime(91))
    print('91 is not a prime number but is is detected as a prime number, based on its field. I see in the field references to number 11 and its multiples.')
    print('prime table: ', prime_table)
    print('calculated primes: ', calc_primes(109))
    print('calc_primes(109)==prime_table: ', calc_primes(109)==prime_table)
    print('however a good approximation. fixing this little imperfection should make it fine.')

    for n in range(1000):
        print(n, end=' ')
        if is_prime(n)!=is_prime_simple(n): print((n, is_prime(n), is_prime_simple(n)))