Pseudoprimes
main page
database
statistics
verification
Database statistics
In the tables below, several counts are listed against thresholds which are powers of 10 and 2.
legend
- #psp: number of (base-2 Fermat) pseudoprimes
- #spsp: number of base-2 strong pseudoprimes
- #carm: number of Carmichael numbers
- #psp-kf: number of pseudoprimes with k factors, not necessarily unique
- green: verified with Sloane's OEIS
- cyan: verified with Galway's 1e15 search
- yellow: NEW results from 2^64 search
- purple: verified against Pinch's list of Carmichael numbers (not just the counts, but the actual numbers)
counts
limit |
#psp |
#spsp |
#carm |
#psp-2f |
#psp-3f |
#psp-4f |
#psp-5f |
#psp-6f |
#psp-7f |
#psp-8f |
#psp-9f |
#psp-10f |
#psp-11f |
#psp-12f |
10^3 |
3 |
0 |
1 |
1 |
2 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
10^4 |
22 |
5 |
7 |
11 |
11 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
10^5 |
78 |
16 |
16 |
34 |
34 |
10 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
10^6 |
245 |
46 |
43 |
107 |
89 |
48 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
10^7 |
750 |
162 |
105 |
312 |
229 |
189 |
20 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
10^8 |
2057 |
488 |
255 |
882 |
485 |
563 |
124 |
3 |
0 |
0 |
0 |
0 |
0 |
0 |
10^9 |
5597 |
1282 |
646 |
2457 |
1105 |
1417 |
563 |
54 |
1 |
0 |
0 |
0 |
0 |
0 |
10^10 |
14884 |
3291 |
1547 |
6504 |
2392 |
3437 |
2133 |
405 |
13 |
0 |
0 |
0 |
0 |
0 |
10^11 |
38975 |
8607 |
3605 |
17206 |
4885 |
7910 |
6847 |
1967 |
156 |
4 |
0 |
0 |
0 |
0 |
10^12 |
101629 |
22407 |
8241 |
46073 |
9951 |
17091 |
19133 |
8198 |
1146 |
37 |
0 |
0 |
0 |
0 |
10^13 |
264239 |
58892 |
19279 |
123868 |
19837 |
35262 |
49484 |
29072 |
6307 |
407 |
2 |
0 |
0 |
0 |
10^14 |
687007 |
156251 |
44706 |
334567 |
38555 |
69972 |
120249 |
91894 |
28607 |
3091 |
72 |
0 |
0 |
0 |
10^15 |
1801533 |
419489 |
105212 |
915443 |
74525 |
134604 |
274978 |
268942 |
113647 |
18505 |
882 |
7 |
0 |
0 |
10^16 |
4744920 |
1135860 |
246683 |
2520503 |
141221 |
252347 |
600418 |
730490 |
400368 |
91948 |
7497 |
128 |
0 |
0 |
10^17 |
12604009 |
3115246 |
585355 |
7002043 |
266025 |
460162 |
1260086 |
1870409 |
1296305 |
398352 |
48833 |
1787 |
7 |
0 |
10^18 |
33763684 |
8646507 |
1401644 |
19604493 |
499285 |
819978 |
2548821 |
4548930 |
3906179 |
1553128 |
266372 |
16301 |
197 |
0 |
10^19 |
91210364 |
24220195 |
3381806 |
55264235 |
932680 |
1430833 |
4994156 |
10581444 |
11073027 |
5545221 |
1268622 |
117068 |
3066 |
12 |
2^64 |
118968378 |
31894014 |
4279356 |
72875460 |
1100575 |
1654895 |
5943968 |
13157498 |
14476538 |
7677426 |
1884450 |
191526 |
6017 |
25 |
limit |
#psp |
#spsp |
#carm |
#psp-2f |
#psp-3f |
#psp-4f |
#psp-5f |
#psp-6f |
#psp-7f |
#psp-8f |
#psp-9f |
#psp-10f |
#psp-11f |
#psp-12f |
2^9 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^10 |
3 |
0 |
1 |
1 |
2 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^11 |
8 |
1 |
3 |
3 |
5 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^12 |
13 |
3 |
5 |
6 |
7 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^13 |
19 |
4 |
6 |
10 |
9 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^14 |
32 |
6 |
9 |
15 |
16 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^15 |
45 |
7 |
10 |
21 |
21 |
3 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^16 |
64 |
11 |
15 |
29 |
27 |
8 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^17 |
89 |
18 |
19 |
38 |
37 |
14 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^18 |
124 |
24 |
23 |
54 |
51 |
19 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^19 |
175 |
34 |
33 |
74 |
71 |
30 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^20 |
251 |
49 |
45 |
108 |
93 |
49 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^21 |
361 |
75 |
55 |
153 |
128 |
77 |
3 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^22 |
502 |
104 |
69 |
212 |
168 |
113 |
9 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^23 |
693 |
147 |
95 |
288 |
219 |
169 |
17 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^24 |
944 |
210 |
130 |
392 |
277 |
249 |
26 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^25 |
1264 |
296 |
162 |
537 |
342 |
338 |
47 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2^26 |
1713 |
409 |
214 |
734 |
426 |
466 |
86 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
2^27 |
2361 |
552 |
290 |
1017 |
541 |
645 |
154 |
4 |
0 |
0 |
0 |
0 |
0 |
0 |
2^28 |
3169 |
734 |
375 |
1368 |
694 |
857 |
241 |
9 |
0 |
0 |
0 |
0 |
0 |
0 |
2^29 |
4232 |
981 |
483 |
1872 |
874 |
1088 |
371 |
26 |
1 |
0 |
0 |
0 |
0 |
0 |
2^30 |
5749 |
1311 |
656 |
2530 |
1130 |
1445 |
585 |
58 |
1 |
0 |
0 |
0 |
0 |
0 |
2^31 |
7750 |
1736 |
864 |
3390 |
1448 |
1895 |
891 |
122 |
4 |
0 |
0 |
0 |
0 |
0 |
2^32 |
10403 |
2314 |
1118 |
4552 |
1799 |
2482 |
1347 |
216 |
7 |
0 |
0 |
0 |
0 |
0 |
2^33 |
14011 |
3093 |
1446 |
6130 |
2275 |
3253 |
1979 |
363 |
11 |
0 |
0 |
0 |
0 |
0 |
2^34 |
18667 |
4139 |
1874 |
8167 |
2806 |
4219 |
2859 |
591 |
25 |
0 |
0 |
0 |
0 |
0 |
2^35 |
24958 |
5511 |
2437 |
10916 |
3499 |
5426 |
4077 |
982 |
58 |
0 |
0 |
0 |
0 |
0 |
2^36 |
33389 |
7396 |
3130 |
14686 |
4360 |
6963 |
5713 |
1559 |
107 |
1 |
0 |
0 |
0 |
0 |
2^37 |
44540 |
9835 |
4058 |
19780 |
5383 |
8825 |
7914 |
2413 |
220 |
5 |
0 |
0 |
0 |
0 |
2^38 |
59565 |
13106 |
5188 |
26624 |
6675 |
11137 |
10915 |
3792 |
412 |
10 |
0 |
0 |
0 |
0 |
2^39 |
79343 |
17493 |
6642 |
35800 |
8246 |
14036 |
14750 |
5786 |
705 |
20 |
0 |
0 |
0 |
0 |
2^40 |
105659 |
23270 |
8521 |
47951 |
10232 |
17612 |
19934 |
8653 |
1236 |
41 |
0 |
0 |
0 |
0 |
2^41 |
141147 |
31115 |
11002 |
64572 |
12585 |
22044 |
26827 |
12950 |
2056 |
113 |
0 |
0 |
0 |
0 |
2^42 |
188231 |
41664 |
14236 |
86981 |
15515 |
27482 |
35689 |
18870 |
3498 |
196 |
0 |
0 |
0 |
0 |
2^43 |
250568 |
55763 |
18400 |
117094 |
19080 |
33899 |
47095 |
27234 |
5801 |
364 |
1 |
0 |
0 |
0 |
2^44 |
333737 |
74739 |
23631 |
157920 |
23379 |
41797 |
61846 |
38768 |
9344 |
674 |
9 |
0 |
0 |
0 |
2^45 |
445316 |
100342 |
30521 |
213096 |
28538 |
51614 |
80984 |
55114 |
14701 |
1245 |
24 |
0 |
0 |
0 |
2^46 |
593366 |
134559 |
39376 |
287244 |
34834 |
63212 |
105340 |
77505 |
22881 |
2295 |
55 |
0 |
0 |
0 |
2^47 |
792172 |
180725 |
50685 |
388120 |
42536 |
77333 |
136272 |
108297 |
35456 |
4046 |
112 |
0 |
0 |
0 |
2^48 |
1059097 |
243566 |
65590 |
525795 |
51856 |
94352 |
175464 |
150198 |
54196 |
7014 |
221 |
1 |
0 |
0 |
2^49 |
1416055 |
327731 |
84817 |
711898 |
63342 |
114695 |
224626 |
207378 |
81587 |
12045 |
481 |
3 |
0 |
0 |
2^50 |
1893726 |
441270 |
109857 |
964378 |
77017 |
139280 |
286631 |
283708 |
121563 |
20144 |
998 |
7 |
0 |
0 |
2^51 |
2532703 |
594585 |
141892 |
1307094 |
93358 |
168844 |
363723 |
385557 |
179071 |
33090 |
1944 |
22 |
0 |
0 |
2^52 |
3390284 |
803252 |
183507 |
1773539 |
113169 |
203818 |
460110 |
520546 |
261524 |
53841 |
3691 |
46 |
0 |
0 |
2^53 |
4540673 |
1085426 |
237217 |
2406877 |
137209 |
245555 |
580223 |
699186 |
378958 |
85744 |
6811 |
110 |
0 |
0 |
2^54 |
6086093 |
1468777 |
307278 |
3270608 |
165900 |
294724 |
728526 |
933728 |
544484 |
135566 |
12298 |
259 |
0 |
0 |
2^55 |
8167163 |
1988905 |
398506 |
4448556 |
200637 |
353452 |
911948 |
1241637 |
777097 |
211557 |
21721 |
557 |
1 |
0 |
2^56 |
10964612 |
2697846 |
517446 |
6053126 |
243026 |
422956 |
1136610 |
1641722 |
1101782 |
326265 |
37869 |
1252 |
4 |
0 |
2^57 |
14731767 |
3662239 |
672105 |
8242376 |
294048 |
505363 |
1412574 |
2161576 |
1551164 |
497454 |
64609 |
2590 |
13 |
0 |
2^58 |
19806649 |
4976375 |
873109 |
11230617 |
355643 |
602341 |
1748734 |
2831153 |
2171208 |
753070 |
108751 |
5098 |
34 |
0 |
2^59 |
26651383 |
6767707 |
1136472 |
15314091 |
429736 |
715537 |
2159388 |
3693298 |
3018375 |
1131002 |
179968 |
9894 |
94 |
0 |
2^60 |
35893886 |
9212942 |
1479525 |
20897619 |
519171 |
849039 |
2659255 |
4798144 |
4173409 |
1684077 |
294405 |
18530 |
237 |
0 |
2^61 |
48374139 |
12552513 |
1927138 |
28531318 |
627361 |
1005938 |
3264147 |
6208781 |
5739850 |
2486163 |
475949 |
34086 |
545 |
1 |
2^62 |
65247459 |
17114780 |
2513234 |
38979638 |
756873 |
1188830 |
3996527 |
8004645 |
7851180 |
3645678 |
761111 |
61712 |
1261 |
4 |
2^63 |
88069251 |
23355139 |
3278553 |
53282196 |
912379 |
1403683 |
4879795 |
10280354 |
10685945 |
5309299 |
1203085 |
109679 |
2825 |
11 |
2^64 |
118968378 |
31894014 |
4279356 |
72875460 |
1100575 |
1654895 |
5943968 |
13157498 |
14476538 |
7677426 |
1884450 |
191526 |
6017 |
25 |