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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?

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!

No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts A remark re OEIS | Comment 7 of 10 |
If any of the solvers intends to submit a sequence to OEIS the qualifying entries  should be either the  quantities of solutions for each group of n-digit  primes i.e.2,2,15,56 ...etc or the 1st generating prime in each group.

  Posted by Ady TZIDON on 2019-07-30 02:46:43
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