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Little explorations with HP calculators (no Prime)
01-13-2019, 01:48 PM (This post was last modified: 01-13-2019 04:56 PM by Albert Chan.)
Post: #345
RE: Little explorations with HP calculators (no Prime)
Code:
Spoiler alert!










Brute force way:
lst = range(1,9)
while len(lst) > 1: lst = [ i*j for i,j in zip(lst, lst[1:]) ]
print float(lst[0]) ==> 6.64903611914e+80

Distribution way:
Final number should have a binomial distribution of factors:
1 and 8: 1 times
2 and 7: 7 times
3 and 6: 7*6/2 = 21 times
4 and 5: 21*5/3 = 35 times

print 8. * 14**7 * 18**21 * 20**35 ==> 6.64903611914e+80

If only required to confirm above number > 1e80:

X = 8 * (14*18*18*18)**7 * 20**35 > 8 * (16**4)**7 * 2**35 * 1e35

log10(X) > log10(2) * (3 + 4*4*7 + 35) + 35 > 0.301 * 150 + 35 = 80.15 > 80
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RE: Little explorations with HP calculators (no Prime) - Albert Chan - 01-13-2019 01:48 PM



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