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Little explorations with HP calculators (no Prime)
01-13-2019, 01:44 PM
Post: #344
RE: Little explorations with HP calculators (no Prime)
Code:
Spoiler alert!










Using the HP-48GX:

{ 1 2 3 4 5 6 7 8 }
« 1 7
  START 2
    « *
    » DOSUBS
  NEXT
»
{ 6.64903611917E80 }


Using binomial coefficients the product can be written as:

1^1 * 2^7 * 3^21 * 4^35 * 5^35 * 6^21 * 7^7 * 8^1 =
8^1 * 14^7 * 18^21 * 20^35 =
6.64903611913E80


Using the common logarithm we can calculate:

 8:    0.90309 *  1 =  0.90309
14:    1.14613 *  7 =  8.02290
18:    1.25527 * 21 = 26.36072
20:    1.30103 * 35 = 45.53605
                      --------
                      80.82276

Even if we only knew the common logarithm of 2, 3 and 7 we can still calculate the needed values:

 2:    0.30103
 3:    0.47712
 7:    0.84510

 8:    0.90309 = 3 * 0.30103
 9:    0.95424 = 2 * 0.47712
18:    1.25527 = 0.95424 + 0.30103
14:    1.14613 = 0.84510 + 0.30103
20:    1.30103 = 1 + 0.30103

So the number is not smaller than 10^80.
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RE: Little explorations with HP calculators (no Prime) - Thomas Klemm - 01-13-2019 01:44 PM



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