CHALLENGE : TRUNCATABLE PRIMES 💻⌨️🖱️

Question

Truncatable prime is a prime number that when you successively remove digits from one end of the prime, you are left with a new prime number.

Examples:

997 is called a left-truncatable prime as the numbers 997, 97, and 7 are all prime.

7393 is a right-truncatable prime as the numbers 7393, 739, 73, and 7 formed by removing digits from its right are also prime.

The task is to find the largest left-truncatable and right-truncatable primes less than 1.000.000
No zeroes are allowed in truncatable prime.

Answer 1

For example :
https://code.sololearn.com/c17zdi9D81wP/?ref=app

Answer 2

//not some different logic😕
//mine initial logic failed ... worst ever logic thinked in the world
https://code.sololearn.com/cYs5Ya0eIDQ0/?ref=app

Answer 3

Thamk you @LukArToDo for your interesting challenge!
Here is my try using C++:

https://code.sololearn.com/c83F40F4QiiY/?ref=app

Answer 4

My try
https://code.sololearn.com/c5Fva8hYpS2N/?ref=app

Answer 5

**** (It's updated !!) ***
https://code.sololearn.com/cBAl5Z6BL562/?ref=app

Answer 6

Thanks to @LukArToDo
https://code.sololearn.com/cZfL32RGCNqj/?ref=app

Answer 7

https://code.sololearn.com/cAnygWXudpqC/?ref=app

Answer 8

Gives largest left and right truncatable primes less than or equal to input number https://code.sololearn.com/cD3zpw9Sv8B9/?ref=app

Answer 9

@LukArTodo : I love this kind of challenges - congrats!

got a simiiar solution like VcC

leftTruncated Prime:
a 2-digit must end with 3 or 7 and has to be a prime
this set is p2

a 3-digit has to end with a p2 and be a prime
this set is p3....

finally this is my prog

https://code.sololearn.com/cWRktOr1RYlU/?ref=app

Answer 10

Why go for millions when you can do billions or trillions ? just enter number of digits (6 to answer the question but higher values work up to 12 digits or 1000000000000)

https://code.sololearn.com/caFQAfueLj5s/?ref=app

Answer 11

choose r or l for left- or righttruncated primes

righttruncated:
prefix must be a right truncated prime
last digit must be 1,3,7,9 otherwise cant be a prime
prefix *10 + last digit must be a prime

build 2-digit prefix and derive valid 3-digit prefix and derive 4digit prefix...

left truncated:: see other post

https://code.sololearn.com/cF6SPX5Yxlxl

Answer 12

I've learned a lot solving this challenge . Especially how to reduce time cost. Thanks everyone.

https://code.sololearn.com/clHC44CsgF5j/?ref=app

Answer 13

My try:
https://code.sololearn.com/c9R77urqXQ7z/#java

Answer 14

Using LINQ 😊

https://code.sololearn.com/cJ1wQgV350hc

Answer 15

My answer
https://code.sololearn.com/cA3WCaaqD2mP/?ref=app

Answer 16

My try :

https://code.sololearn.com/W9fPINXqI33I/?ref=app

Answer 17

Also for lefttruncatable Primes there can be done something:

crossSum must never become devisible by 3
So eg the crossSum of a number is 2, next number may not be 4,7,9
So we can shorten runtime

Tried it by a dynamic generator for demonstrazion

https://code.sololearn.com/cvnTZflUFyQx

Answer 18

I found an interesting attribute of right-truncated primes:
They may only have digits 1,3,7,9 so far...

additionally:
The sum of digit 7 and digit 1 must be one or two
- Exactly one digit 7 and no digit 1
- One digit 7 and one digit 1
- Two digits 7 and no digit 1
- Two digits 1 and no digit 7

This comes from checking if 3 is a devisor via crosssum
9 and 3 are neutral

7 and 1 mod 3 is 2
so as soon as you have the third digit(1,7) the number is devisible by 3.

With this knowledge I could shorten runtime a bit
https://code.sololearn.com/c7Ud5wbbRwIo

Answer 19

my try
https://code.sololearn.com/cbsp7AM8myyl/?ref=app

Answer 20

####UPDATED#####
After all that 'Time Limit exceeds' finally it is done....
https://code.sololearn.com/cErf0NLJTvcV/?ref=app