A076150 10k+1,3,7,9.

[Don McDonald]

>  
>  2.MZD02-Sep.10k+1379
>  2.MZD02-Sep.10k1,3,7,9  this file.


Prod{10*k+i};i=1,3,7,9
has all its prime factors less than 3.4 *k.

confirmed k =  20 32 51 53 62 84 ,...

Hence (all composite decade +1.)
{10*k} + 0,1,2,3,4,5,6,7,8,9,10.

e.g. odd cannot usually have factor 2.
if odd has factor 3, then the cofactor is
approximately (less than?)  10*k/3 < 3.4*k

don.mcdonald at paradise.net.nz
02.11.02  22:49  nz dt.

my file > *ram.sumryfact.creditcd1..  Sat,02 Nov 2002.22:33:20
by don.mcdonald.pgm.c22A. BBC Basic64.Risc os.Acorn Archimedes comp 1990.

(prob) -- #formula,--  value, --   FACTORS -- ,  (centiseconds).
---   ---   ---   ---   ---   ---   ---   ---   ---   
2  (10*prob+1)*(10*prob..=378189= 3*3*3*3*7*23*29*all?n 2cs
3  (10*prob+1)*(10*prob..=1476189= 3*3*11*13*31*37*all?n 2cs
4  (10*prob+1)*(10*prob..=4060189= 7*7*41*43*47*all?n 2cs
5  (10*prob+1)*(10*prob..=9090189= 3*3*17*19*53*59*all?n 2cs
6  (10*prob+1)*(10*prob..=17766189= 3*3*3*7*23*61*67*all?n 2cs
7  (10*prob+1)*(10*prob..=31528189= 7*11*71*73*79*all?n 2cs
8  (10*prob+1)*(10*prob..=52056189= 3*3*3*3*3*29*83*89*all?n 2cs
9  (10*prob+1)*(10*prob..=81270189= 3*3*3*7*11*13*31*97*all?n 2cs
10  (10*prob+1)*(10*prob..=121330189= 101*103*107*109*all?n 2cs
11  (10*prob+1)*(10*prob..=174636189= 3*3*3*7*13*17*37*113*all?n 2cs
12  (10*prob+1)*(10*prob..=243828189= 3*3*11*11*41*43*127*all?n 2cs
13  (10*prob+1)*(10*prob..=331786189= 7*19*131*137*139*all?n 3cs
14  (10*prob+1)*(10*prob..=441630189= 3*3*7*7*11*13*47*149*all?n 2cs
15  (10*prob+1)*(10*prob..=576720189= 3*3*3*17*53*151*157*all?n 3cs
16  (10*prob+1)*(10*prob..=740656189= 7*13*13*23*163*167*all?n 3cs
continu.
17  (10*prob+1)*(10*prob..=937278189= 3*3*3*19*59*173*179*all?n 3cs
18  (10*prob+1)*(10*prob..=1170666189= 3*3*3*3*7*11*17*61*181*all?n 2cs
19  (10*prob+1)*(10*prob..=1445140189= 191*193*197*199*all?n 3cs
20*  (10*prob+1)*(10*prob..=1765260189= 3*3*3*7*11*19*23*29*67*all?n 2cs
21  (10*prob+1)*(10*prob..=2135826189= 3*3*7*31*71*73*211*all?n 2cs
22  (10*prob+1)*(10*prob..=2561878189= 13*17*223*227*229*all 4cs
23  (10*prob+1)*(10*prob..=3048696189= 3*7*11*3*79*233*239*all 4cs
24  (10*prob+1)*(10*prob..=3601800189= 3*13*19*3*3*3*3*3*83*241*all 3cs
25  (10*prob+1)*(10*prob..=4226950189= 7*11*23*37*251*257*all 4cs
26  (10*prob+1)*(10*prob..=4930146189= 3*3*3*29*89*263*269*all 4cs
27  (10*prob+1)*(10*prob..=5717628189= 3*7*13*3*3*31*271*277*all 4cs
28  (10*prob+1)*(10*prob..=6595876189= 7*17*17*41*281*283*all 5cs
29  (10*prob+1)*(10*prob..=7571610189= 3*11*13*23*3*3*3*97*293*all 4cs
30  (10*prob+1)*(10*prob..=8651790189= 3*7*3*43*101*103*307*all 3cs
31  (10*prob+1)*(10*prob..=9843616189= 11*29*311*313*317*all 5cs
32*  (10*prob+1)*(10*prob..=11154528189= 3*7*17*19*3*47*107*109*all 4cs
33  (10*prob+1)*(10*prob..=12592206189= 3*3*3*37*113*331*337*all 5cs
34  (10*prob+1)*(10*prob..=14164570189= 7*11*7*7*31*347*349*all 5cs
35  (10*prob+1)*(10*prob..=15879780189= 3*7*13*17*3*3*3*353*359*all 5cs
36  (10*prob+1)*(10*prob..=17746236189= 3*11*19*3*3*11*19*41*367*all 3cs
continu.
37  (10*prob+1)*(10*prob..=19772578189= 7*13*29*53*373*379*all 5cs
38  (10*prob+1)*(10*prob..=21967686189= 3*3*3*43*127*383*389*all 5cs
39  (10*prob+1)*(10*prob..=24340680189= 3*7*17*19*23*3*131*397*all 3cs
40  (10*prob+1)*(10*prob..=26900920189= 11*13*31*37*401*409*all 5cs
41  (10*prob+1)*(10*prob..=29658006189= 3*7*3*59*137*139*419*all 4cs
42  (10*prob+1)*(10*prob..=32621778189= 3*7*11*13*3*3*47*61*421*all 3cs
43  (10*prob+1)*(10*prob..=35802316189= 19*23*431*433*439*all 5cs
44  (10*prob+1)*(10*prob..=39209940189= 3*7*3*3*7*149*443*449*all 5cs
45  (10*prob+1)*(10*prob..=42855210189= 3*11*17*3*3*3*41*151*457*all 4cs
46  (10*prob+1)*(10*prob..=46748926189= 7*67*461*463*467*all 6cs
47  (10*prob+1)*(10*prob..=50902128189= 3*11*3*3*43*53*157*479*all 4cs
48  (10*prob+1)*(10*prob..=55326096189= 3*7*13*23*3*37*163*487*all 4cs
49  (10*prob+1)*(10*prob..=60032350189= 7*17*29*71*491*499*all 5cs
50  (10*prob+1)*(10*prob..=65032650189= 3*13*3*13*167*503*509*all 6cs
51*  (10*prob+1)*(10*prob..=70338996189= 3*7*11*19*3*3*3*47*73*173*all 3cs
52  (10*prob+1)*(10*prob..=75963628189= 17*23*23*31*521*523*all 6cs
53*  (10*prob+1)*(10*prob..=81919026189= 3*7*11*13*3*3*7*41*59*179*all 4cs
54  (10*prob+1)*(10*prob..=88217910189= 3*3*3*61*181*541*547*all 7cs
55  (10*prob+1)*(10*prob..=94873240189= 7*13*19*29*43*79*557*all 3cs
56  (10*prob+1)*(10*prob..=101898216189= 3*7*11*17*3*3*3*3*563*569*all 6cs
continu.
57  (10*prob+1)*(10*prob..=109306278189= 3*3*191*193*571*577*all 9cs
58  (10*prob+1)*(10*prob..=117111106189= 7*11*19*31*53*83*587*all 3cs
59  (10*prob+1)*(10*prob..=125326620189= 3*3*197*199*593*599*all 10cs
60  (10*prob+1)*(10*prob..=133966980189= 3*7*3*3*29*67*601*607*all 7cs
61  (10*prob+1)*(10*prob..=143046586189= 13*47*613*617*619*all 7cs
62*  (10*prob+1)*(10*prob..=152580078189= 3*7*11*17*19*23*3*3*3*37*89*all 3cs
63  (10*prob+1)*(10*prob..=162582336189= 3*7*13*3*3*7*71*211*631*all 4cs
64  (10*prob+1)*(10*prob..=173068480189= 11*59*641*643*647*all 7cs
65  (10*prob+1)*(10*prob..=184053870189= 3*7*3*3*31*73*653*659*all 7cs
66  (10*prob+1)*(10*prob..=195554106189= 3*13*17*23*3*29*223*661*all 4cs
67  (10*prob+1)*(10*prob..=207585028189= 7*11*61*97*673*677*all 7cs
68  (10*prob+1)*(10*prob..=220162716189= 3*13*3*53*227*229*683*all 4cs
69  (10*prob+1)*(10*prob..=233303490189= 3*7*11*17*3*3*41*233*691*all 4cs
70  (10*prob+1)*(10*prob..=247023910189= 7*19*37*101*701*709*all 7cs
71  (10*prob+1)*(10*prob..=261340776189= 3*23*3*3*31*79*239*719*all 5cs
72  (10*prob+1)*(10*prob..=276271128189= 3*7*3*3*3*3*3*3*103*241*727*all 5cs
73  (10*prob+1)*(10*prob..=291832246189= 11*17*43*67*733*739*all 7cs
74  (10*prob+1)*(10*prob..=308041650189= 3*7*13*19*3*3*83*107*743*all 4cs
75  (10*prob+1)*(10*prob..=324917100189= 3*11*23*3*251*751*757*all 6cs
76  (10*prob+1)*(10*prob..=342476596189= 7*13*59*109*761*769*all 8cs
continu.
77  (10*prob+1)*(10*prob..=360738378189= 3*7*19*3*37*41*257*773*all 5cs
78  (10*prob+1)*(10*prob..=379720926189= 3*11*3*3*3*29*71*263*787*all 5cs
79  (10*prob+1)*(10*prob..=399442960189= 7*13*17*47*61*113*797*all 4cs
80  (10*prob+1)*(10*prob..=419923440189= 3*11*3*3*73*89*269*809*all 5cs
81  (10*prob+1)*(10*prob..=441181566189= 3*7*13*19*3*3*43*271*811*all 4cs
82  (10*prob+1)*(10*prob..=463236778189= 821*823*827*829*all 21cs
83  (10*prob+1)*(10*prob..=486108756189= 3*7*17*3*3*3*7*31*277*839*all 4cs
84*  (10*prob+1)*(10*prob..=509817420189= 3*7*11*3*11*29*29*281*283*all 5cs
contin.