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@Hermann-SW

Hermann-SW/M500000500001.gp

Created December 23, 2024 14:24
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PARI/GP proof that Mersenne exponent 500000500001 does not give Mersenne prime (291.0g resident memory needed)
Raw
M500000500001.gp
m=2^500000500001-1;
##
d=2 * 1663403835355 * 500000500001 + 1;
##
m%d
##
#binary(d)
##
@Hermann-SW
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Execution of script on old Xeon server with 384GB RAM:

hermann@e5-2680:~$ time gp -q < M500000500001.gp 
  ***   last result computed in 39,079 ms.
  ***   last result computed in 0 ms.
0
  ***   last result computed in 1min, 9,606 ms.
81
  ***   last result computed in 0 ms.

real	4m19.189s
user	1m59.203s
sys	2m19.966s
hermann@e5-2680:~$

@Hermann-SW
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Virtual and resident memory logging for gp, started before previous comment execution.
First output of above execution happened when 2:28.11 was reported below.
Maximal 528.5g virtual and 291.0g resident memory(!):

hermann@e5-2680:~$ top -b | grep " gp"
  27679 hermann   20   0  353.9g  35984   4624 R   0.7   0.0   0:00.02 gp
  27679 hermann   20   0  353.9g   5.4g   4624 R 100.0   1.4   0:03.04 gp
  27679 hermann   20   0  353.9g  10.7g   4624 R  99.7   2.8   0:06.06 gp
  27679 hermann   20   0  353.9g  16.1g   4624 R 100.0   4.3   0:09.09 gp
  27679 hermann   20   0  353.9g  21.5g   4624 R 100.0   5.7   0:12.11 gp
  27679 hermann   20   0  353.9g  26.8g   4624 R 100.0   7.1   0:15.14 gp
  27679 hermann   20   0  353.9g  32.2g   4624 R  99.3   8.5   0:18.15 gp
  27679 hermann   20   0  353.9g  37.6g   4624 R 100.0  10.0   0:21.18 gp
  27679 hermann   20   0  353.9g  42.9g   4624 R 100.0  11.4   0:24.20 gp
  27679 hermann   20   0  353.9g  48.2g   4624 R 100.0  12.8   0:27.22 gp
  27679 hermann   20   0  353.9g  53.5g   4624 R 100.0  14.2   0:30.25 gp
  27679 hermann   20   0  353.9g  58.8g   4688 R  99.7  15.6   0:33.26 gp
  27679 hermann   20   0  353.9g  64.0g   4688 R  99.7  17.0   0:36.28 gp
  27679 hermann   20   0  353.9g  69.1g   4688 R 100.0  18.3   0:39.31 gp
  27679 hermann   20   0  353.9g  74.3g   4688 R 100.0  19.7   0:42.33 gp
  27679 hermann   20   0  353.9g  79.4g   4688 R 100.0  21.1   0:45.36 gp
  27679 hermann   20   0  353.9g  84.6g   4688 R 100.0  22.4   0:48.38 gp
  27679 hermann   20   0  353.9g  89.7g   4688 R  99.7  23.8   0:51.39 gp
  27679 hermann   20   0  353.9g  94.8g   4688 R 100.0  25.1   0:54.42 gp
  27679 hermann   20   0  353.9g  99.9g   4688 R 100.0  26.5   0:57.45 gp
  27679 hermann   20   0  353.9g 105.0g   4688 R  99.7  27.8   1:00.47 gp
  27679 hermann   20   0  353.9g 110.1g   4688 R 100.0  29.2   1:03.49 gp
  27679 hermann   20   0  353.9g 115.2g   4688 R 100.0  30.5   1:06.51 gp
  27679 hermann   20   0  412.1g 120.5g   4688 R  99.7  31.9   1:09.53 gp
  27679 hermann   20   0  412.1g 125.9g   4688 R 100.0  33.4   1:12.55 gp
  27679 hermann   20   0  412.1g 131.2g   4688 R 100.0  34.8   1:15.58 gp
  27679 hermann   20   0  412.1g 136.6g   4688 R 100.0  36.2   1:18.60 gp
  27679 hermann   20   0  412.1g 142.0g   4688 R 100.0  37.6   1:21.62 gp
  27679 hermann   20   0  412.1g 147.3g   4688 R 100.0  39.0   1:24.65 gp
  27679 hermann   20   0  412.1g 152.5g   4688 R 100.0  40.4   1:27.67 gp
  27679 hermann   20   0  412.1g 157.8g   4688 R 100.0  41.8   1:30.69 gp
  27679 hermann   20   0  412.1g 163.1g   4688 R 100.0  43.2   1:33.72 gp
  27679 hermann   20   0  412.1g 168.3g   4688 R  99.7  44.6   1:36.74 gp
  27679 hermann   20   0  412.1g 173.6g   4688 R 100.0  46.0   1:39.76 gp
  27679 hermann   20   0  412.1g 174.6g   4688 R 100.0  46.3   1:42.78 gp
  27679 hermann   20   0  412.1g 174.6g   4688 R 100.0  46.3   1:45.81 gp
  27679 hermann   20   0  412.1g 174.6g   4688 R  99.7  46.3   1:48.83 gp
  27679 hermann   20   0  470.3g 177.7g   4752 R 100.0  47.1   1:51.85 gp
  27679 hermann   20   0  470.3g 183.1g   4752 R 100.0  48.5   1:54.87 gp
  27679 hermann   20   0  470.3g 188.4g   4752 R 100.0  49.9   1:57.89 gp
  27679 hermann   20   0  470.3g 192.7g   4752 R 100.0  51.1   2:00.92 gp
  27679 hermann   20   0  470.3g 197.0g   4752 R  99.7  52.2   2:03.93 gp
  27679 hermann   20   0  470.3g 201.2g   4752 R 100.0  53.3   2:06.96 gp
  27679 hermann   20   0  470.3g 205.5g   4752 R 100.0  54.5   2:09.98 gp
  27679 hermann   20   0  470.3g 209.7g   4752 R  99.7  55.6   2:13.00 gp
  27679 hermann   20   0  470.3g 213.9g   4752 R 100.0  56.7   2:16.03 gp
  27679 hermann   20   0  470.3g 218.1g   4752 R  99.7  57.8   2:19.04 gp
  27679 hermann   20   0  470.3g 222.4g   4752 R 100.0  59.0   2:22.07 gp
  27679 hermann   20   0  470.3g 226.6g   4752 R  99.7  60.1   2:25.09 gp
  27679 hermann   20   0  470.3g 230.9g   4752 R 100.0  61.2   2:28.11 gp
  27679 hermann   20   0  528.5g 234.9g   4940 R 100.0  62.3   2:31.14 gp
  27679 hermann   20   0  528.5g 238.8g   4940 R 100.0  63.3   2:34.16 gp
  27679 hermann   20   0  528.5g 242.6g   4940 R 100.0  64.3   2:37.19 gp
  27679 hermann   20   0  528.5g 246.5g   4940 R  99.7  65.3   2:40.20 gp
  27679 hermann   20   0  528.5g 250.3g   4940 R 100.0  66.4   2:43.23 gp
  27679 hermann   20   0  528.5g 254.2g   4940 R  99.7  67.4   2:46.24 gp
  27679 hermann   20   0  528.5g 258.0g   4940 R 100.0  68.4   2:49.27 gp
  27679 hermann   20   0  528.5g 261.9g   4940 R  99.7  69.4   2:52.29 gp
  27679 hermann   20   0  528.5g 265.7g   4940 R 100.0  70.4   2:55.32 gp
  27679 hermann   20   0  528.5g 269.5g   4940 R  99.7  71.5   2:58.33 gp
  27679 hermann   20   0  528.5g 273.4g   4940 R 100.0  72.5   3:01.35 gp
  27679 hermann   20   0  528.5g 277.3g   4940 R 100.0  73.5   3:04.38 gp
  27679 hermann   20   0  528.5g 281.2g   4940 R  99.7  74.5   3:07.40 gp
  27679 hermann   20   0  528.5g 285.1g   4940 R 100.0  75.6   3:10.42 gp
  27679 hermann   20   0  528.5g 289.0g   4940 R 100.0  76.6   3:13.45 gp
  27679 hermann   20   0  528.5g 291.0g   4940 R 100.0  77.2   3:16.47 gp
  27679 hermann   20   0  528.5g 291.0g   4940 R 100.0  77.2   3:19.49 gp
  27679 hermann   20   0  528.5g 291.0g   4940 R  99.7  77.2   3:22.51 gp
  27679 hermann   20   0  528.5g 291.0g   4940 R 100.0  77.2   3:25.54 gp
  27679 hermann   20   0  528.5g 291.0g   4940 R  99.7  77.2   3:28.55 gp
  27679 hermann   20   0  528.5g 291.0g   4940 R 100.0  77.2   3:31.58 gp
  27679 hermann   20   0  528.5g 291.0g   4940 R 100.0  77.2   3:34.61 gp
  27679 hermann   20   0  528.5g 291.0g   4940 R  99.3  77.2   3:37.62 gp
  27679 hermann   20   0  528.5g 291.0g   4940 R 100.0  77.2   3:40.65 gp
  27679 hermann   20   0  528.5g 291.0g   4940 R 100.0  77.2   3:43.67 gp
  27679 hermann   20   0  528.5g 291.0g   5064 R  99.7  77.2   3:46.68 gp
  27679 hermann   20   0  528.5g 291.0g   5064 R 100.0  77.2   3:49.71 gp
  27679 hermann   20   0  528.5g 291.0g   5064 R 100.0  77.2   3:52.73 gp
  27679 hermann   20   0  528.5g 291.0g   5064 R 100.0  77.2   3:55.76 gp
  27679 hermann   20   0  528.5g 291.0g   5064 R  99.7  77.2   3:58.77 gp
  27679 hermann   20   0  528.5g 291.0g   5064 R 100.0  77.2   4:01.80 gp
  27679 hermann   20   0  528.5g 291.0g   5064 R  99.7  77.2   4:04.82 gp
  27679 hermann   20   0  528.5g 291.0g   5064 R 100.0  77.2   4:07.84 gp
  27679 hermann   20   0  528.5g 291.0g   5064 R 100.0  77.2   4:10.86 gp
  27679 hermann   20   0  470.3g 189.0g   5188 R 100.0  50.1   4:13.88 gp
  27679 hermann   20   0  353.9g  81.0g   5252 R 100.0  21.5   4:16.90 gp
^C
hermann@e5-2680:~$

@Hermann-SW
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With this PARI/GP config:

hermann@e5-2680:~$ grep parisize /etc/gprc | grep -v '\\'
parisizemax = 380G
parisize = 380G
hermann@e5-2680:~$

@Hermann-SW
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Script above is useless, can be computed in 3ms on slow Raspberry computer with not much RAM:

pi@raspberrypi5:~ $ gp -q
?
? d=2 * 1663403835355 * 500000500001 + 1;
? Mod(2,d)^500000500001 - 1
Mod(0, 1663405498762162162670711)
? ##
  ***   last result: cpu time 0 ms, real time 3 ms.
?

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