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Find the sum of all Truncatable primes below N in Python
Suppose we have a given integer N; we have to find the sum of all Truncatable primes less than N. As we know the truncatable prime is a number which is left-truncatable prime (if the leading "left" digit is successively removed, then all resulting numbers are treated as prime) as well as right-truncatable prime (if the last "right" digit is successively removed, then all the resulting numbers are treated as prime). An example of truncatable prime is 9137 as this is lefttruncatable prime because 9137, 137, 37 and 7 are primes. Hence 9137 is a truncatable prime.
So, if the input is like N = 55, then the output will be 130 as (2 + 3 + 5 + 7 + 23 + 37 + 53) =
To solve this, we will follow these steps −
N := 1000005
prime := a list of size N and fill with True
Define a function sieve() . This will take
prime[1] := False, prime[0] := False
for i in range 2 to N, do
if prime[i] is same as True, then
for j in range i * 2 to N, update in each step by i, do
prime[j] := False
From the main method, do the following −
sum := 0
for i in range 2 to n, do
current := i
f := True
while current is non-zero, do
if prime[current] is False, then
f := False
come out from the loop
current := current / 10
current := i
power := 10
while quotient of (current / power) is non-zero, do
if prime[current mod power] is False, then
f := False
come out from the loop
power := power * 10
if f is True, then
sum := sum + i
return sum
Example
Let us see the following implementation to get better understanding −
N = 1000005 prime = [True for i in range(N)] def sieve(): prime[1] = False prime[0] = False for i in range(2, N): if (prime[i]==True): for j in range(i * 2, N, i): prime[j] = False def get_total_of_trunc_primes(n): sum = 0 for i in range(2, n): current = i f = True while (current): if (prime[current] == False): f = False break current //= 10 current = i power = 10 while (current // power): if (prime[current % power] == False): f = False break power *= 10 if f: sum += i return sum n = 55 sieve() print(get_total_of_trunc_primes(n))
Input
55
Output
130
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