[sci.math.research] Carmichael numbers up to 10^16

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Article #2433

#2433

From: Richard Pinch
Date: Wed, 14 Oct 1992 11:58

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Archive-name: auto/sci.math.research/Carmichael-numbers-up-to-10-16

CARMICHAEL NUMBERS UP TO 10^16 (preliminary announcement)

There are 246683 Carmichael numbers up to 10^16.
I hope this list is complete, but it has not yet
been completely checked.

The list is avilable by anonymous FTP from 131.111.24.28,
can.pmms.cam.ac.uk, in file /pub/Carmichael/carmichael-16.

Richard Pinch
Dept of Pure Mathematics
University of Cambridge
16 Mill Lane
Cambridge  CB2 1SB
U.K.

5 October 1992 15:50

The number of Carmichael numbers less than M with k prime factors:

  k   10^12   10^13   10^14   10^15   10^16
  -   -----   -----   -----   -----   -----
  3    1000    1858    3284    6083   10816
  4    2102    3639    6042    9938   16202
  5    3156    7082   14938   29282   55012
  6    1714    5270   14401   36907   86696
  7     262    1340    5359   19210   60150
  8       7      89     655    3622   16348
  9       0       1      27     170    1436
 10       0       0       0       0      23
 11       0       0       0       0       0
 12       0       0       0       0       0
 13       0       0       0       0       0
      -----   -----   -----   -----   -----
       8241   19279   44706  105212  246683


The ratio C(10^n)/C(10^n-1)

  n   C(10^n) C(10^n-1)  ratio
  -    ------    ------  -----
  4         7         1  7.000
  5        16         7  2.286
  6        43        16  2.688
  7       105        43  2.441
  8       255       105  2.429
  9       646       255  2.533
 10      1547       646  2.395
 11      3605      1547  2.330
 12      8241      3605  2.286
 13     19279      8241  2.339
 14     44706     19279  2.319
 15    105212     44706  2.353
 16    246683    105212  2.345

The function k(x) of Pomerance/Selfridge/Wagstaff

  n    k(x)
  -  -------
  3  2.93319
  4  2.19547
  5  2.07632
  6  1.97946
  7  1.93388
  8  1.90495
  9  1.87989
 10  1.86870
 11  1.86421
 12  1.86377
 13  1.86240
 14  1.86293
 15  1.86301
 16  1.86406

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From: rgep@emu.pmms.cam.ac.uk (Richard Pinch)
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Subject: [sci.math.research] Carmichael numbers up to 10^16
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