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The NASCAR Prime Puzzle:There are 40 permissible 2digit endings for prime numbers. Consider the following "race" after the first 1000 primes: 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!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, ... Proposed by G. L. Honaker, Jr. (June 2016)
Submitted: 20160722 20:49:02; Last Modified: 20180211 12:40:00.
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