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Pairs of primes (Posted on 2019-07-27) Difficulty: 4 of 5
Imagine a bag containing cards representing all n-digit odd numbers. A random card is drawn and two new numbers are created by preceding the drawn number by each of its even neighbors.

What is the probability that each of those 2 numbers is prime?

Examples:
For n=1 there are 5 cards i.e. 1,3,5,7 and 9. Clearly only numbers 3 and 9 qualifiy since fboth 23 and 43 are primes and so are 89 and 109 & there are no other answers. So for n=1 p=0.4 is the probability we were looking for.
For n=2 I will not provide the answer but will show you one of the qualifying numbers e.g. 69, since both 6869 and 7069 are prime.

Now evaluate the correct probabilities for n=2,3, ...8,9 (or as far as your resources allow) - and you will get a sequence for which you may be credited @ OEIS.

So this time you get a task both challenging and rewarding!
GOOD LUCK...

No Solution Yet Submitted by Ady TZIDON    
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Comments: ( You must be logged in to post comments.)
  Subject Author Date
An extensionCharlie2019-07-31 10:50:14
re(2): via computer - the start of the solnSteven Lord2019-07-30 17:00:40
Hints/TipsRe how far can one goAdy TZIDON2019-07-30 02:56:30
Some ThoughtsA remark re OEISAdy TZIDON2019-07-30 02:46:43
a note re further computer searchesxdog2019-07-28 19:07:49
re: via computer - the start of the solnCharlie2019-07-28 07:58:12
re(2): computer solution through n=6 list continuedCharlie2019-07-27 22:01:14
re: computer solution through n=6 list continuedCharlie2019-07-27 22:00:18
Solutioncomputer solution through n=6Charlie2019-07-27 21:57:42
via computer - the start of the solnSteven Lord2019-07-27 13:16:57
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