Based on this youtube video... https://youtu.be/azL5ehbw_24. Which deals with left truncating prime numbers.

Left_Trunc_Primes.py

#   Title:          left_trunc_prime.py
#   Description:    This is a generator of left truncating prime numbers.  Each
#                   number in the 'all_primes' list will have the property of 
#                   being a prime number after the left most digit is truncated.
#                   For example, the prime number 137 is such a left truncating 
#                   prime.  If you truncate the 1, the number 37 is also a prime
#                   number, if you truncate the 3, the number 7 is a prime 
#                   number.
#
#                   If run successfully, the result should be a list of 1,442 
#                   endpoints (largest base numbers that cannot have another 
#                   digit added to the left and still meet the defintion of a 
#                   left truncating prime).  The largest endpoint should be 
#                   357,686,312,646,216,567,629,137.
#
#                   The program was run using single core processor, single 
#                   threading on a 3.2GHz Intel Core i5 Mac.  During the run 
#                   time, the single core processor ran >95%.  Results are 
#                   appended at the end.
#  Author:          Bill Armstrong
#  Date:            July 29, 2018
#  Version:         1.0
#  Usage:           python left_trunc_prime.py
#  Notes:           
#  Python_version:  3.6.4
####################################################################################

import math
import time

def is_prime(num):
    if(num==1):
        return False
    if(num==2):
        return True
    if(num%2==0):
        return False

    i = 3
    while(i<math.sqrt(num)+1):
        if num%i==0:
            return False
        i += 2
    return True

primes = [2, 3, 5, 7]
endpoints = []
all_primes = []
num = [1, 2, 3, 4, 5, 6, 7, 8, 9]

t = time.time()

while len(primes)>0:
    ep = True
    base = primes.pop(0)
    all_primes.append(base)
    for leftnum in num:
        test_num = int(str(leftnum) + str(base))
        if is_prime(test_num):
            print("prime found: ", test_num)
            primes.append(test_num)
            all_primes.append(test_num)
            ep = False
    if ep:
        endpoints.append(base)
        print("endpoint found:  ", base, "  Total endpoints:  ", 
            len(endpoints), "  Total primes left to check:  ", len(primes))

print ("*** COMPLETE ***")
print ("Found", len(endpoints), "endpoints.")
print ("With a total of", len(all_primes), 
    "prime numbers that have the Left Trunc property.")
print ("The largest Left Trunc prime was:  ", endpoints[-1])
print ("Total processing time was", (time.time()- t), ".")

#  Terminal Output of lines 54 - 58
'''
*** COMPLETE ***
Found 1442 endpoints.
With a total of 8516 prime numbers that have the Left Trunc property.
The largest Left Trunc prime was:   357686312646216567629137
Total processing time was 440014.46286058426 .

Largest left truc number:  357,686,312,646,216,567,629,137
Total time:  5 days, 2 hours,  13 minutes, 34.46286058425903 seconds

The last 5 endpoints:

endpoint found:   315396334245663786197   Total endpoints:   1437   Total primes left to check:   5
endpoint found:   666276812967623946997   Total endpoints:   1438   Total primes left to check:   4
prime found:  96686312646216567629137
prime found:  57686312646216567629137
prime found:  95918918997653319693967
endpoint found:   9918918997653319693967   Total endpoints:   1439   Total primes left to check:   3
endpoint found:   96686312646216567629137   Total endpoints:   1440   Total primes left to check:   2
prime found:  357686312646216567629137
endpoint found:   95918918997653319693967   Total endpoints:   1441   Total primes left to check:   1
endpoint found:   357686312646216567629137   Total endpoints:   1442   Total primes left to check:   0
'''

Future modifications...

a) Try multithreading on prime calculations
b) Try multiprocessor on prime calculations