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...
(Program was corrected for bug noticed by Charlie.)
dig prob
-----------
1 0.5000
2 0.0455
3 0.0334
4 0.0124
5 0.0089
6 0.0050
To get more would require downloading a many Gbyte file of known primes, which seems (sorry - no insult intended) like a bit of a fool's errand...
program prr
use iso_fortran_env
implicit none
real rat
integer(kind=int64)::i,j,k,l,twop,odds,b1,b2,k1,k2,flag
do i = 1,13
twop=0
odds=0
b1=10**(i-1)+1
if (i.eq.1)b1=1
b2=10**i-1
do j = b1,b2,2
odds=odds+1
k1=j+(j-1)*10**i
k2=j+(j+1)*10**i
call isprime(k1,flag)
if (flag.eq.1)then
call isprime(k2,flag)
if(flag.eq.1)twop=twop+1
endif
enddo
rat=1.*twop/(1.*odds)
print 1,i,rat
1 format(i2,2x,f6.4)
enddo
end
subroutine isprime(i,n)
use iso_fortran_env
implicit none
integer (kind=int64)::i,j,k,l,m,n
n=1
if(i.eq.2)return
n=0
k=sqrt(1.*i)
do j=2,k
m=i/j
l=m*j
if(l.eq.i)go to 1
enddo
n=1
1 return
end
Edited on July 30, 2019, 5:03 pm
via computer - the start of the soln
