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There are 40 permissible 2-digit endings for prime numbers. Consider the following "race" after the first 1000 primes:
Let a(n) = the number of primes that end with "01" among the first 10^n primes.
The sequence begins 0, 2, 25, ...

Let a(n) = the number of primes that end with "03" among the first 10^n primes.
The sequence begins 0, 2, 25, ...

Let a(n) = the number of primes that end with "07" among the first 10^n primes.
The sequence begins 0, 2, 27, ...

Let a(n) = the number of primes that end with "09" among the first 10^n primes.
The sequence begins 0, 3, 24, ...

Let a(n) = the number of primes that end with "11" among the first 10^n primes.
The sequence begins 1, 3, 25, ... 

Let a(n) = the number of primes that end with "13" among the first 10^n primes.
The sequence begins 1, 3, 23, ...

Let a(n) = the number of primes that end with "17" among the first 10^n primes.
The sequence begins 1, 2, 25, ...

Let a(n) = the number of primes that end with "19" among the first 10^n primes.
The sequence begins 1, 2, 27, ...

Let a(n) = the number of primes that end with "21" among the first 10^n primes.
The sequence begins 0, 2, 27, ...

Let a(n) = the number of primes that end with "23" among the first 10^n primes. 
The sequence begins 1, 3, 28, ...

Let a(n) = the number of primes that end with "27" among the first 10^n primes. 
The sequence begins 0, 2, 23, ...

Let a(n) = the number of primes that end with "29" among the first 10^n primes.
The sequence begins 1, 2, 26, ...

Let a(n) = the number of primes that end with "31" among the first 10^n primes.
The sequence begins 0, 4, 24, ...

Let a(n) = the number of primes that end with "33" among the first 10^n primes.
The sequence begins 0, 2, 24, ...

Let a(n) = the number of primes that end with "37" among the first 10^n primes. 
The sequence begins 0, 3, 25, ...

Let a(n) = the number of primes that end with "39" among the first 10^n primes. 
The sequence begins 0, 3, 23, ...

Let a(n) = the number of primes that end with "41" among the first 10^n primes.
The sequence begins 0, 3, 21, ...

Let a(n) = the number of primes that end with "43" among the first 10^n primes.
The sequence begins 0, 2, 24, ...

Let a(n) = the number of primes that end with "47" among the first 10^n primes.
The sequence begins 0, 2, 26, ...

Let a(n) = the number of primes that end with "49" among the first 10^n primes.
The sequence begins 0, 3, 23, ...

Let a(n) = the number of primes that end with "51" among the first 10^n primes.
The sequence begins 0, 2, 28, ...

Let a(n) = the number of primes that end with "53" among the first 10^n primes.
The sequence begins 0, 2, 27, ...

Let a(n) = the number of primes that end with "57" among the first 10^n primes.
The sequence begins 0, 3, 29, ...

Let a(n) = the number of primes that end with "59" among the first 10^n primes.
The sequence begins 0, 2, 26, ...

Let a(n) = the number of primes that end with "61" among the first 10^n primes.
The sequence begins 0, 2, 23, ...

Let a(n) = the number of primes that end with "63" among the first 10^n primes.
The sequence begins 0, 3, 23, ...

Let a(n) = the number of primes that end with "67" among the first 10^n primes.
The sequence begins 0, 4, 25, ...

Let a(n) = the number of primes that end with "69" among the first 10^n primes.
The sequence begins 0, 1, 22, ...

Let a(n) = the number of primes that end with "71" among the first 10^n primes.
The sequence begins 0, 2, 23, ...

Let a(n) = the number of primes that end with "73" among the first 10^n primes.
The sequence begins 0, 3, 27, ...

Let a(n) = the number of primes that end with "77" among the first 10^n primes.
The sequence begins 0, 1, 25, ...

Let a(n) = the number of primes that end with "79" among the first 10^n primes.
The sequence begins 0, 4, 26, ...

Let a(n) = the number of primes that end with "81" among the first 10^n primes.
The sequence begins 0, 2, 24, ...

Let a(n) = the number of primes that end with "83" among the first 10^n primes.
The sequence begins 0, 3, 27, ...

Let a(n) = the number of primes that end with "87" among the first 10^n primes.
The sequence begins 0, 1, 23, ...

Let a(n) = the number of primes that end with "89" among the first 10^n primes.
The sequence begins 0, 2, 25, ...

Let a(n) = the number of primes that end with "91" among the first 10^n primes.
The sequence begins 0, 2, 25, ...

Let a(n) = the number of primes that end with "93" among the first 10^n primes.
The sequence begins 0, 2, 24, ...

Let a(n) = the number of primes that end with "97" among the first 10^n primes.
The sequence begins 0, 3, 25, ...

Let a(n) = the number of primes that end with "99" among the first 10^n primes.
The sequence begins 0, 2, 24, ...
Clearly, we have "Car Number 57" in the lead with 29 primes after 1000 laps (primes). But what about after 10000 laps? 100000 laps? 10^25 laps? Place your bets now!
Proposed by G. L. Honaker, Jr. (June 2016)

 

  Submitted: 2016-07-22 20:49:02;   Last Modified: 2017-08-13 20:40:48.



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