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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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re(2): computer solution through n=6 list continued | Comment 4 of 10 |
(In reply to re: computer solution through n=6 list continued by Charlie)

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 972291 972290972291 972292972291
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 978201 978200978201 978202978201
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 980043 980042980043 980044980043
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 982731 982730982731 982732982731
 982893 982892982893 982894982893
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 986481 986480986481 986482986481
 986631 986630986631 986632986631
 987393 987392987393 987394987393
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 992013 992012992013 992014992013
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 994089 994088994089 994090994089
 994173 994172994173 994174994173
 995433 995432995433 995434995433
 996777 996776996777 996778996777
 997491 997490997491 997492997491
 997647 997646997647 997648997647
 997689 997688997689 997690997689
 997851 997850997851 997852997851
 998067 998066998067 998068998067
 998391 998390998391 998392998391
 998643 998642998643 998644998643
 999039 999038999039 999040999039
 999999 999998999999 1000000999999
 2231 


  Posted by Charlie on 2019-07-27 22:01:14
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