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def prime_no(a):
    for i in range(2,a-1):
        if a%i ==0: 
            return False
    return True

def firstfact(a):
     if prime_no(a):
          return(a)
     factor=0
     for i in range(2,a):
            if a%i==0:
                factor=i
                return factor
                break

def factorise(number,firstprime):
        factorlist=[]
        count=0
        factorlist.append(firstprime)
        if prime_no(number):
             return(factorlist)
        while True:
            number=int(number/firstfact(number))
            if prime_no(number):
                factorlist.append(number)
                return(factorlist)
                break
            factorlist.append(firstfact(number))

factorisation=[]


for i in range(2,21):
    number=i
    firstprime=firstfact(number)
    factored=factorise(number,firstprime)
    print(factored)
    if set(factored).issubset(set(factorisation)):
        print("yes this is happening")
        continue
    else:
         for v in factored:
              if v not in factorisation:
                   factorisation.append(v)
           
print(factorisation)



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from math import sqrt

def prime_no(a):
    for i in range(2,a-1):
        if a%i ==0: 
            return False
    return True

def firstfact(a):
     factor=0
     for i in range(2,(int(sqrt(a))+1)):
        if prime_no(i):
            if a%i==0:
                factor=i
                return factor
                break
   



powers=[""]

for i in range(20):
    a=i
    if prime_no(i):
        powers.append(i)
    else:
     
        ()