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...
(In reply to
re: computer solution through n=6 list continued by Charlie)
970851 970850970851 970852970851
970947 970946970947 970948970947
971073 971072971073 971074971073
972279 972278972279 972280972279
972291 972290972291 972292972291
972399 972398972399 972400972399
973191 973190973191 973192973191
973917 973916973917 973918973917
975129 975128975129 975130975129
975477 975476975477 975478975477
975633 975632975633 975634975633
976053 976052976053 976054976053
977361 977360977361 977362977361
978117 978116978117 978118978117
978201 978200978201 978202978201
979047 979046979047 979048979047
979173 979172979173 979174979173
979293 979292979293 979294979293
979587 979586979587 979588979587
979833 979832979833 979834979833
979893 979892979893 979894979893
980043 980042980043 980044980043
981087 981086981087 981088981087
981141 981140981141 981142981141
981981 981980981981 981982981981
982731 982730982731 982732982731
982893 982892982893 982894982893
983817 983816983817 983818983817
984129 984128984129 984130984129
984291 984290984291 984292984291
984507 984506984507 984508984507
984513 984512984513 984514984513
985593 985592985593 985594985593
986301 986300986301 986302986301
986319 986318986319 986320986319
986481 986480986481 986482986481
986631 986630986631 986632986631
987393 987392987393 987394987393
987957 987956987957 987958987957
989079 989078989079 989080989079
989277 989276989277 989278989277
989613 989612989613 989614989613
989673 989672989673 989674989673
990051 990050990051 990052990051
990201 990200990201 990202990201
991311 991310991311 991312991311
992013 992012992013 992014992013
992451 992450992451 992452992451
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
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Posted by Charlie
on 2019-07-27 22:01:14 |
re(2): computer solution through n=6 list continued
