A 5-digit base-N prime number P is such that we will obtain three other prime numbers by changing its first digit.
Determine the minimum value of N.
For N =
base 6, 10001 (1297 in decimal) makes 3 other primes if the first digit is changed.
base 6 10001
base 6 ['10001', '20001', '30001', '50001']
decimal [1297, 2593, 3889, 6481]
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def base2base(n,a,b):
""" input n which is a string of the number to be changed
'a' is an integer representing the current base
to be changed to base b
"""
def dec2base(i,base):
""" INPUT integer in base 10, return string
of Base base equivalent. """
convertString = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'
if i < base:
return convertString[i]
else:
return dec2base(i//base,base) + convertString[i%base]
if a == 10:
return dec2base(int(n),b)
if b == 10:
return int(str(n),a)
elif b != 10:
return base2base(int(str(n),a),10,b)
def isprime(n):
'''check if integer n is a prime'''
n = abs(int(n))
if n < 2:
return False
if n == 2:
return True
if not n & 1:
return False
for x in range(3, int(n**0.5)+1, 2):
if n % x == 0:
return False
return True
base = 6
digits = [str(i) for i in range(base)]
bot = base**(4)
top = base**5
primes = [base2base(n, 10, base) for n in range(bot,top) if isprime(n)]
for p in primes:
count = 0
baselist = []
decilist = []
for d in digits:
test = d + p[1:]
if test in primes:
count += 1
baselist.append(test)
decilist.append(base2base(test,base,10))
if count >= 4:
print('base', base, p)
print(baselist)
print(decilist)
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Posted by Larry
on 2023-07-17 09:36:55 |
Solution
