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Run Example
(%i1)ggg(n):=f([a:eval_string("n"), x:charlist(string(n)),b:(sum(eval_string(part(x,k)),k,1,length(x)))])*(is(equal(primep(a)*primep(b),true^2))-unknown)/(true-unknown);
(%o1) ggg(n) := (f([a : eval_string("n"), x : charlist(string(n)), 
b : sum(eval_string(part(x, k)), k, 1, length(x))])
                                    2
 (is(equal(primep(a) primep(b), true )) - unknown))/(true - unknown)
(%i2) sum(ggg(n),n,1,1000);
(%o2) f([991, [9, 9, 1], 19]) + f([977, [9, 7, 7], 23])
 + f([971, [9, 7, 1], 17]) + f([953, [9, 5, 3], 17]) + f([937, [9, 3, 7], 19])
 + f([919, [9, 1, 9], 19]) + f([911, [9, 1, 1], 11]) + f([887, [8, 8, 7], 23])
 + f([883, [8, 8, 3], 19]) + f([881, [8, 8, 1], 17]) + f([863, [8, 6, 3], 17])
 + f([829, [8, 2, 9], 19]) + f([827, [8, 2, 7], 17]) + f([823, [8, 2, 3], 13])
 + f([821, [8, 2, 1], 11]) + f([809, [8, 0, 9], 17]) + f([797, [7, 9, 7], 23])
 + f([773, [7, 7, 3], 17]) + f([757, [7, 5, 7], 19]) + f([751, [7, 5, 1], 13])
 + f([739, [7, 3, 9], 19]) + f([733, [7, 3, 3], 13]) + f([719, [7, 1, 9], 17])
 + f([683, [6, 8, 3], 17]) + f([661, [6, 6, 1], 13]) + f([647, [6, 4, 7], 17])
 + f([643, [6, 4, 3], 13]) + f([641, [6, 4, 1], 11]) + f([607, [6, 0, 7], 13])
 + f([601, [6, 0, 1], 7]) + f([599, [5, 9, 9], 23]) + f([593, [5, 9, 3], 17])
 + f([577, [5, 7, 7], 19]) + f([571, [5, 7, 1], 13]) + f([557, [5, 5, 7], 17])
 + f([487, [4, 8, 7], 19]) + f([467, [4, 6, 7], 17]) + f([463, [4, 6, 3], 13])
 + f([461, [4, 6, 1], 11]) + f([449, [4, 4, 9], 17]) + f([443, [4, 4, 3], 11])
 + f([421, [4, 2, 1], 7]) + f([409, [4, 0, 9], 13]) + f([401, [4, 0, 1], 5])
 + f([397, [3, 9, 7], 19]) + f([379, [3, 7, 9], 19]) + f([373, [3, 7, 3], 13])
 + f([359, [3, 5, 9], 17]) + f([353, [3, 5, 3], 11]) + f([337, [3, 3, 7], 13])
 + f([331, [3, 3, 1], 7]) + f([317, [3, 1, 7], 11]) + f([313, [3, 1, 3], 7])
 + f([311, [3, 1, 1], 5]) + f([283, [2, 8, 3], 13]) + f([281, [2, 8, 1], 11])
 + f([269, [2, 6, 9], 17]) + f([263, [2, 6, 3], 11]) + f([241, [2, 4, 1], 7])
 + f([229, [2, 2, 9], 13]) + f([227, [2, 2, 7], 11]) + f([223, [2, 2, 3], 7])
 + f([199, [1, 9, 9], 19]) + f([197, [1, 9, 7], 17]) + f([193, [1, 9, 3], 13])
 + f([191, [1, 9, 1], 11]) + f([179, [1, 7, 9], 17]) + f([173, [1, 7, 3], 11])
 + f([157, [1, 5, 7], 13]) + f([151, [1, 5, 1], 7]) + f([139, [1, 3, 9], 13])
 + f([137, [1, 3, 7], 11]) + f([131, [1, 3, 1], 5]) + f([113, [1, 1, 3], 5])
 + f([101, [1, 0, 1], 2]) + f([89, [8, 9], 17]) + f([83, [8, 3], 11])
 + f([67, [6, 7], 13]) + f([61, [6, 1], 7]) + f([47, [4, 7], 11])
 + f([43, [4, 3], 7]) + f([41, [4, 1], 5]) + f([29, [2, 9], 11])
 + f([23, [2, 3], 5]) + f([11, [1, 1], 2]) + f([7, [7], 7]) + f([5, [5], 5])
 + f([3, [3], 3]) + f([2, [2], 2])
(%i3) 
Run Example
product(sum(f(n,(10*k+1),10*n-(2*k+1))*(is(equal(primep((2*k+1))*primep(2*n-(2*k+1)),true^2))-unknown)/(true-unknown),k, 18000, 19000),n,10^30,10^30);
(%o1) f(1000000000000000000000000000000, 189751, 
9999999999999999999999999962049) + f(1000000000000000000000000000000, 185011, 
9999999999999999999999999962997)
(%i2) 
Run Example
makelist(sum((f(n,k,n-k)*(is(equal(primep(k)*primep(n-k),true^2))-unknown)/(true-unknown)),k,0,n),n,2,10);
(%o1) [0, 0, f(4, 2, 2), f(5, 3, 2) + f(5, 2, 3), f(6, 3, 3), 
f(7, 5, 2) + f(7, 2, 5), f(8, 5, 3) + f(8, 3, 5), f(9, 7, 2) + f(9, 2, 7), 
f(10, 7, 3) + f(10, 5, 5) + f(10, 3, 7)]
(%i2) 

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