Palindrome Post Party!

[DeaconBrews]

13231!

 

[Bronson Pinchot]

1001

 

[DeaconSlim2.0]

 

[HailToTheDeacons]

9,999

 

[HailToTheDeacons]

And 10,001.

 

[grendel]

 

[discdude]

1111 HOLLLA

 

[lbE08]

 

[lbE08]

can't find a picture of 12221 so here's one of adam scott.

 

[Deacon923]

2222 FTMFW.

 

[TownieDeac]

15051

 

[TownieDeac]

15051

16561

thats 1510 posts in 6 weeks...eesh

 

[Deaconblue]

141

The Air Force workhorse transport plane.

 

[TownieDeac]

16561

thats 1510 posts in 6 weeks...eesh

17171

that's ~43 posts per day since the last update

 

[Deacon923]

missed the last several opportunities.

 

[TownieDeac]

17171

that's ~43 posts per day since the last update

18381

down to ~35 ppd

 

[deacdiggler]

Math: do palindrome posts become more rare as you increase your count?

I would think so. In the hundreds, every 10th post is a palindrome. In the thousands it's every 110 posts. In the ten thousands it's every 100 posts or so. In the hundred thousands is where it would really be an occasion - every 1100 posts or so I think.

Is there a mathematical way to prove this out?

 

[TownieDeac]

Math: do palindrome posts become more rare as you increase your count?

I would think so. In the hundreds, every 10th post is a palindrome. In the thousands it's every 110 posts. In the ten thousands it's every 100 posts or so. In the hundred thousands is where it would really be an occasion - every 1100 posts or so I think.

Is there a mathematical way to prove this out?

import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Random;

public class PalindromicPrimeFinder implements Runnable {

/**
* Test main
*/
public static void main(String[] args) {

int maxDepth = 50;
int testCertainty = 20;
Character[] digitsFinal = { '1', '7' }; // should be a subset of {1, 3, 7, 9}
Character[] digitsAll = { '1', '7' };
PrintWriter writer = new PrintWriter(System.out);

PalindromicPrimeFinder finder = new PalindromicPrimeFinder(
maxDepth, testCertainty, digitsFinal, digitsAll, writer);

finder.run();

}


private final Random random = new Random();

private final int maxDepth;
private final int testCertainty;
private final Character[] digitsFinal;
private final Character[] digitsAll;
private final PrintWriter writer;


/**
* Constructor.
*
* @param start The starting number
* @param maxDepth Max search depth
* @param testCertainty Certainty of primality test
* @param digitsFinal final digits (subset of {1, 3, 7, 9})
* @param digitsAll all digits
*/
public PalindromicPrimeFinder(int maxDepth,
int testCertainty, Character[] digitsFinal, Character[] digitsAll,
PrintWriter writer) {
this.maxDepth = maxDepth;
this.testCertainty = testCertainty;
this.digitsFinal = digitsFinal;
this.digitsAll = digitsAll;
this.writer = writer;
}


/**
* Run method
*/
@Override
public void run() {
String start = ""+digitsFinal[random.nextInt(digitsFinal.length)];
findPalindromicPrime(start, 0);
}

/**
* Worker recursive method
* @param number current number
* @param depth current depth
*/
private void findPalindromicPrime(String number, int depth) {

for (char digit : digitsFinal) {
String nextNumber = digit + number + digit;
if (new BigInteger(nextNumber).isProbablePrime(testCertainty)) {
writer.println("New prime [length=" + nextNumber.length()
+ "]: " + nextNumber + "\n");
writer.flush();
findPalindromicPrime(nextNumber, 0);
return;
}
}

if (depth > maxDepth) {
return;
}

List<Character> digitsAll_shuffled = new ArrayList<Character>(
Arrays.asList(digitsAll));
Collections.shuffle(digitsAll_shuffled, random);
for (char digit : digitsAll_shuffled) {
String nextNumber = digit + number + digit;
findPalindromicPrime(nextNumber, depth + 1);
}

}

}

 

[TownieDeac]

 

[TownieDeac]

the first of those is a java hack that can generate a 1000 digit palindrome made of only prime numbers

the second is a proof that all even number of digits palindromes are divisible by 11.