101 is the smallest prime whose sum of the digits i.e.
2 is less than the number of its digits (
3).
Compile a list of all primes below 10^10 with this feature.
101
10111
20011
20101
21001
100003
100103
101021
101111
102001
102101
103001
120011
121001
200003
200201
201011
201101
202001
210011
210101
1000003
1000121
1000211
1001003
1002101
1003001
1010003
1010201
1011001
1020001
1020011
1020101
1021001
1100101
1102001
1120001
1201001
2000003
2001101
2002001
2020001
2100001
2100011
2110001
3001001
3010001
10000103
10000121
10000141
10000303
10001203
10001221
10001311
10001401
10002121
10003001
10003003
10010023
10010101
10010113
10010311
10010401
10011013
10011101
10011121
10011301
10012001
10012021
10012111
10013011
10020013
10020103
10020121
10021001
10021003
10021111
10022011
10023001
10030003
10040011
10100011
10100113
10100131
10100201
10100221
10101101
10102003
10102201
10103011
10110011
10111001
10112101
10113001
10120021
10120111
10130101
10140001
10200011
10200101
10200301
10201001
10203001
10210111
10220011
10220101
10300201
10301101
10310101
11000111
11000113
11000401
11001013
11001031
11001103
11001301
11002001
11003011
11010211
11011003
11011201
11012011
11020001
11020003
11021011
11030011
11100013
11100101
11100121
11110111
11110201
11111101
11130001
11200001
11201101
11210011
11300101
12001001
12001021
12001111
12010021
12021001
12100003
12100111
12100201
12102001
12110101
12120001
12200011
13000201
13001101
13200001
20000003
20000023
20000221
20000311
20001001
20001031
20001301
20002201
20004001
20011001
20012011
20012101
20020001
20030011
20101001
20101201
20111011
20130001
20200111
20201101
20210101
20211001
20300011
20300101
20310001
21000103
21000121
21001021
21002101
21003001
21010111
21020011
21021001
21030001
21100003
21100021
22000001
22000003
22000021
22000201
22001101
22011001
22110001
22200001
23000011
23000101
23100001
24000001
30000001
30000301
30001003
30001201
30010021
30011101
30100003
30100111
30100201
30200011
30210001
31000003
31002001
31020001
31100011
31100101
32000011
32001001
32010001
33000001
40000003
40000021
40010011
40010101
40011001
41000101
41001001
50000101
50010001
100000007
100000123
100000213
100000223
100000231
100000421
100001131
100001203
100001303
100002011
100002013
100002031
100002103
100002113
100003021
100003301
100005001
100010021
100010023
100010033
100010051
100010203
100010231
100010321
100010401
100011031
100011113
100011203
100012103
100012111
100012301
100013021
100020023
100020103
100020113
100020121
100020131
100021003
100021121
100022003
100022201
100023101
100030001
100030121
100031003
100031011
100031101
100032011
100040011
100040201
100042001
100050001
100050101
100060001
100100051
100100111
100100401
100101013
100101041
100101121
100101203
100101401
100102021
100103111
100105001
100110013
100110041
100110121
100111001
100111003
100112101
100113001
100113011
100120003
100121011
100121111
100121201
100130003
100131001
100131011
100140011
100200011
100200013
100200031
100200301
100201103
100201201
100201301
100202101
100203001
100210001
100211021
100211101
100220101
100221101
100230001
100300001
100300121
100310003
100330001
100401011
100401101
100500011
101000023
101000051
101000113
101000203
101000231
101000311
101000401
101001001
101001011
101001013
101001041
101002021
101002103
101002301
101003101
101004011
101005001
101010031
101010113
101011013
101011121
101011301
101020111
101021003
101030021
101030101
101040001
101100011
101100113
101100211
101101103
101101111
101102003
101102101
101103001
101110013
101110201
101111011
101111111
101120021
101121011
101130101
101201003
101210101
101220001
101230001
101300201
101301001
101320001
102000023
102000131
102000401
102001121
102001201
102002003
102010301
102013001
102020021
102021001
102100001
102100003
102100111
102100211
102100301
102110101
102110111
102120001
102120101
102200011
102200101
102201101
102300001
102310001
103000111
103000201
103000301
103001201
103010003
103020011
103021001
103101001
103110011
103120001
103200101
103201001
104000011
104000021
104000201
104002001
104101001
104110001
105000001
106000001
110000201
110000221
110000411
110001131
110001211
110001301
110002003
110002103
110002111
110002201
110002301
110003011
110004001
110005001
110010013
110010031
110010101
110010113
110010301
110010401
110011103
110012011
110020003
110020301
110021011
110021111
110030201
110032001
110040101
110050001
110100013
110100113
110100121
110100203
110100401
110101001
110101003
110102021
110110201
110111011
110111021
110111201
110113001
110120011
110130001
110131001
110200021
110200121
110200201
110201011
110201101
110201111
110202101
110212001
110220101
110300011
110301001
110301011
110400001
111000031
111000101
111000103
111000401
111001001
111001003
111001201
111002201
111003001
111004001
111010013
111010111
111020003
111020111
111030001
111102011
111200003
111201011
111210101
111300001
112000111
112001011
112010011
112010021
112010201
112021001
112100111
112100201
112110001
112200001
113001011
114000001
114000101
120000031
120000103
120000121
120000203
120000301
120000311
120001001
120001111
120001121
120001201
120002021
120002111
120003001
120003011
120003101
120010201
120010211
120012001
120013001
120020011
120020111
120021101
120040001
120100003
120100103
120101011
120102001
120110201
120130001
120200011
120202001
120210001
120210011
121000003
121000211
121000301
121002001
121011101
121030001
121100003
121100011
121101011
121102001
121200011
122000003
122001001
122001101
122020001
123000011
124000001
130000001
130001111
130002001
130010201
130020101
130030001
130100101
130102001
131000021
131001011
132000101
133000001
140010001
140200001
150000001
150010001
200000033
200000051
200000123
200000131
200000201
200000221
200000321
200001001
200001013
200001103
200001211
200002301
200003003
200004001
200010011
200010121
200010211
200010301
200010311
200011211
200012003
200012201
200013001
200020031
200020103
200020211
200021011
200023001
200030101
200030111
200031001
200031011
200040011
200040101
200100031
200101003
200102003
200102011
200102101
200103011
200110103
200111011
200120201
200121001
200130101
200140001
200200003
200200031
200210111
200211101
200220001
200230001
200300003
200301001
201000211
201000301
201002111
201010001
201011003
201012101
201020011
201020101
201020201
201021101
201100001
201100013
201101003
201102001
201102101
201110201
201121001
201130001
201300101
202000003
202000021
202001003
202002001
202010021
202011011
202012001
202110101
202111001
202200001
203000101
203000201
203010001
203010011
203200001
204000011
204001001
205000001
210000023
210000113
210001003
210001021
210001111
210001301
210003011
210004001
210010001
210010103
210010201
210010301
210011201
210020003
210020101
210021101
210030011
210030101
210040001
210100013
210100211
210110003
210110111
210120101
210121001
210210001
211000021
211000121
211001101
211001201
211002101
211010101
211011011
211020001
211021001
211110101
211111001
211200001
211210001
212000003
212000021
212000101
212001001
212010101
212020001
212110001
213000001
220000013
220000201
220010201
220020011
220030001
220110001
220200011
220300001
221010001
221010011
221020001
221100101
222000101
222001001
230000003
230001011
230010101
230100001
231000101
231010001
240000011
240001001
240100001
300000031
300001001
300001003
300001103
300001211
300001301
300003001
300003101
300010001
300010013
300011021
300012001
300012101
300013001
300020003
300020111
300030001
300100001
300100121
300100301
300101003
300101101
300110011
300111011
300111101
300121001
300130001
300200111
300210101
300300001
300310001
301000013
301000211
301001111
301002001
301002101
301010011
301010201
301011001
301100101
301101001
301102001
301110011
301111001
301200001
301300001
302001001
302010101
302100011
302101001
302110001
303000001
310001011
310001101
310001201
310002101
310010003
310010021
310010201
310011001
310020001
310100101
310101101
310200101
311001011
311010001
311010101
313000001
320000201
320100101
321000011
321100001
330000001
331000001
400000301
400001011
400001101
400001111
400001201
400002011
400003001
400010111
400010201
400021001
400100011
400120001
400201001
400210001
400300001
401000011
401001001
401200001
403000001
410000111
410010001
410010011
410020001
410100101
411000011
420000101
421000001
500000003
500000101
500000201
500001001
501001001
501010001
510000011
510001001
600000001
700000001
1000000007
1000000021
1000000033
1000000103
1000000123
1000000223
1000000241
1000000321
1000000403
1000000411
1000001011
1000001021
1000001203
1000001213
1000001311
1000001501
1000002103
1000003013
1000003111
1000003211
1000005001
1000010051
1000010101
1000010303
1000010321
1000011011
1000011301
1000012121
1000013011
1000013101
1000014011
1000020001
1000020011
1000020023
1000020221
1000021003
1000030001
1000030103
1000030121
1000030301
1000032101
1000040201
1000050001
1000060001
1000100033
1000100051
1000100201
1000100303
1000100401
1000100501
1000102003
1000102121
1000103003
1000103101
1000110101
1000110203
1000110401
1000111103
1000111121
1000111201
1000112011
1000112021
1000120001
1000120021
1000120103
1000130011
1000200001
1000200013
1000200031
1000200101
1000200203
1000201003
1000202003
1000202101
1000204001
1000210301
1000212011
1000213001
1000240001
1000300003
1000300031
1000300121
1000300211
1000302001
1000310011
1000320011
1000400021
1000401001
1000401011
1000410011
1000411001
1000510001
1000600001
1001000051
1001000111
1001000113
1001000131
1001000141
1001000321
1001001011
1001001311
1001002001
1001002111
1001003111
1001004101
1001005001
1001010011
1001010013
1001010103
1001010113
1001010401
1001011003
1001011103
1001011211
1001011301
1001012101
1001020003
1001020021
1001030003
1001030011
1001030101
1001031011
1001040011
1001040101
1001101021
1001101121
1001103001
1001110013
1001110021
1001110031
1001110111
1001112001
1001120101
1001130101
1001200111
1001201101
1001202101
1001210003
1001210101
1001220001
1001300011
1001301101
1001310001
1002000001
1002000101
1002000301
1002001211
1002002021
1002002201
1002010003
1002010013
1002010021
1002010301
1002011011
1002011201
1002021001
1002100013
1002100031
1002101011
1002103001
1002110003
1002110111
1002120101
1002220001
1003000001
1003000021
1003000111
1003000121
1003000211
1003010003
1003010011
1003011011
1003111001
1004000003
1004000111
1004000201
1004010011
1004010101
1004100101
1004101001
1004110001
1005100001
1006000001
1010000011
1010000021
1010000051
1010000111
1010000113
1010000203
1010000231
1010000401
1010001023
1010001101
1010001203
1010002001
1010002031
1010003003
1010003021
1010004011
1010004101
1010010011
1010010013
1010010311
1010011103
1010011111
1010012021
1010020003
1010021021
1010030011
1010040001
1010050001
1010100011
1010100103
1010100121
1010102011
1010102021
1010102101
1010104001
1010110001
1010110103
1010110201
1010111111
1010113001
1010120011
1010120101
1010130101
1010201111
1010201201
1010202001
1010210021
1010212001
1010221001
1010300101
1010300201
1010301001
1010301011
1010310011
1011000041
1011000101
1011001003
1011001031
1011001301
1011003011
1011003101
1011010031
1011010201
1011010211
1011021001
1011030011
1011030101
1011040001
1011100003
1011100121
1011110011
1011110021
1011200011
1011201011
1011301001
1012000013
1012000201
1012001021
1012001101
1012001201
1012002011
1012010101
1012010201
1012021001
1012030001
1012101011
1013000011
1013000101
1013011001
1014000101
1015000001
1020000011
1020000013
1020000103
1020000131
1020000301
1020001001
1020001013
1020001201
1020002111
1020002201
1020010031
1020020201
1020022001
1020030001
1020030101
1020100001
1020100021
1020101003
1020101021
1020102011
1020110111
1020111011
1020200201
1020210101
1020220001
1020310001
1021000103
1021000121
1021002001
1021010101
1021011001
1021011011
1021100011
1021100021
1021101001
1021101101
1021200101
1021300001
1022200001
1023000101
1030000001
1030000021
1030000031
1030000201
1030000211
1030001003
1030001101
1030002011
1030002101
1030010011
1030010101
1030100003
1030110101
1030200001
1031002001
1031011001
1031110001
1032000001
1040000011
1040000201
1040020001
1040100011
1040101001
1041010001
1050000011
1100000051
1100000123
1100000203
1100000401
1100001041
1100001101
1100001121
1100001131
1100001211
1100001401
1100002031
1100003011
1100004011
1100010001
1100010031
1100010103
1100010113
1100011013
1100011021
1100013001
1100020021
1100020211
1100021003
1100030021
1100040001
1100041001
1100050001
1100100041
1100100121
1100101003
1100101111
1100102021
1100104001
1100110211
1100110301
1100111003
1100120003
1100200201
1100203001
1100210021
1100210101
1100211001
1100300021
1100310011
1100400011
1100400101
1101000113
1101000301
1101000311
1101000401
1101001001
1101001021
1101002003
1101002011
1101010111
1101020021
1101020111
1101030001
1101100031
1101100201
1101101201
1101110011
1101200101
1101202001
1101210001
1102000013
1102001003
1102001111
1102010011
1102100011
1102101001
1102110101
1102210001
1103000011
1103000021
1103000111
1103010001
1103020001
1103100101
1103101001
1104010001
1104100001
1110001103
1110002111
1110010201
1110011003
1110011101
1110012011
1110020201
1110031001
1110100031
1110101021
1110110011
1110130001
1110200111
1110201101
1110202001
1110301001
1111003001
1111010003
1111011101
1111020011
1111100021
1111100101
1111110001
1111200001
1112000003
1112000111
1112001001
1112011001
1113000001
1113000101
1120000031
1120001111
1120002001
1120010011
1120012001
1120030001
1120100021
1120110001
1120200101
1120300001
1121000011
1121001001
1121101001
1122000101
1130000101
1130001001
1130001011
1130002001
1130100001
1130110001
1131000011
1140000011
1140000101
1140100001
1200000041
1200000101
1200000121
1200000203
1200000311
1200001001
1200001013
1200002101
1200002201
1200010001
1200010003
1200011201
1200012001
1200012101
1200021101
1200101011
1200103001
1200110011
1200120011
1200200021
1200200101
1200202001
1200210101
1200220001
1200400001
1201000103
1201000121
1201000201
1201000301
1201001003
1201001111
1201010003
1201010201
1201011001
1201011011
1201020101
1201030001
1201100101
1201110101
1202000101
1202000201
1202100001
1203100001
1204000001
1210000013
1210000021
1210000111
1210001003
1210001011
1210001101
1210010101
1210030001
1210110101
1211100101
1212000011
1212001001
1221000101
1230001001
1300000003
1300000021
1300000103
1300000201
1300000301
1300010003
1300021001
1300100111
1300110001
1300110011
1300200101
1300210001
1301000101
1301000201
1301001011
1301010001
1301011001
1301100011
1302000101
1302010001
1303000001
1310000101
1310001101
1310110001
1320000001
1400000101
1400002001
1400010011
1400100011
1400110001
1401000001
1401000101
1500000001
1500000101
2000000011
2000000033
2000000141
2000000203
2000001001
2000001013
2000001103
2000002031
2000010013
2000010041
2000010121
2000011001
2000011031
2000011301
2000014001
2000020103
2000021003
2000021011
2000030111
2000031101
2000040101
2000100131
2000101021
2000101111
2000101211
2000102201
2000110201
2000111021
2000111101
2000111111
2000112011
2000120011
2000121001
2000140001
2000200003
2000200201
2000203001
2000210101
2000211001
2000300021
2000301001
2000301101
2000310001
2000400011
2000500001
2001000013
2001000031
2001000101
2001000301
2001000311
2001001003
2001001103
2001002011
2001003101
2001004001
2001010001
2001011003
2001011101
2001012001
2001020101
2001021101
2001030001
2001040001
2001100001
2001100103
2001100301
2001101101
2001102001
2001102101
2001110201
2001120001
2001200011
2001202001
2001210011
2001400001
2002000031
2002001021
2002002001
2002002011
2002010111
2002011101
2002021001
2002100201
2002201001
2003000201
2003001001
2003001101
2003020001
2004000101
2004100001
2010000001
2010001111
2010001121
2010010003
2010010111
2010011111
2010012001
2010013001
2010020003
2010020021
2010100013
2010100021
2010100201
2010101021
2010102001
2010200201
2010201001
2010210001
2010210011
2010220001
2010300011
2010400001
2011000001
2011000003
2011002001
2011002101
2011010101
2011010201
2011011011
2011012001
2011101101
2011110011
2011111001
2012002001
2012010001
2012010101
2012101001
2020000111
2020000201
2020001201
2020100111
2020102001
2021001001
2021110001
2030100001
2030200001
2031001001
2040000101
2100000011
2100000101
2100000311
2100001021
2100001103
2100001121
2100003011
2100010021
2100010111
2100010301
2100011201
2100012011
2100020003
2100101021
2100101111
2100102001
2100130001
2100201011
2100300001
2100300011
2101000211
2101002011
2101003001
2101010011
2101100011
2101120001
2101200011
2102000101
2102000111
2102100001
2103010001
2110000001
2110000003
2110000031
2110000121
2110000301
2110001021
2110002101
2110020001
2110100101
2110101001
2110110011
2111020001
2111200001
2120011001
2120101001
2130000001
2130100001
2200000031
2200000211
2200001003
2200001021
2200001201
2200010003
2200010011
2200020001
2200101011
2200110001
2200200001
2201100101
2202000001
2202000011
2210000101
2212000001
2300011001
2300020001
2300100001
2301000001
2301000101
2301100001
2400000011
2401000001
2500000001
3000000401
3000001003
3000001031
3000002003
3000010003
3000010031
3000010103
3000010121
3000100031
3000100111
3000102011
3000110011
3000112001
3000201101
3000210011
3000300011
3001000001
3001000031
3001002001
3001010021
3001010101
3001101101
3001102001
3002000101
3002000201
3002001001
3003000001
3010000001
3010000013
3010001003
3010002011
3010100011
3010100111
3010110001
3010110011
3010210001
3011000011
3011001101
3011010011
3011011001
3011110001
3012000011
3012001001
3020000101
3020002001
3020010001
3020110001
3021000001
3030010001
3100000121
3100010003
3100101101
3100300001
3101000003
3101100011
3102000001
3102010001
3110002001
3110011001
3110100011
3110110001
3130000001
3200000201
3200001011
3300000001
3300010001
4000001003
4000001101
4000002001
4000100003
4000100201
4000111001
4000200101
4000201001
4001002001
4001100011
4002000011
4002001001
4002100001
4010200001
4020100001
4030000001
4100001001
4100011001
4101000011
4101100001
4110000001
4110001001
4111000001
4200100001
4210000001
5000001011
5000011001
5002000001
5010010001
5020000001
5100000011
6000000001
6000010001
7000000001
is the sorted output from
DefDbl A-Z
Dim ns As String, digtot, crlf$
Function mform$(x, t$)
a$ = Format$(x, t$)
If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
mform$ = a$
End Function
Private Sub Form_Load()
Text1.Text = ""
crlf$ = Chr(13) + Chr(10)
Form1.Visible = True
For d1 = 1 To 8
digtot = d1: ns = LTrim(Str(d1))
addOn 2
Next
Text1.Text = Text1.Text & crlf & "done" & crlf
End Sub
Sub addOn(wh)
For newdig = 0 To 7
c$ = LTrim(Str(newdig))
digtot = digtot + newdig
ns = ns + c
If digtot <= 9 Then
If digtot < Len(ns) Then
v = Val(ns)
If prmdiv(v) = v Then
Text1.Text = Text1.Text & mform(v, "###########") & crlf
DoEvents
End If
End If
If wh < 10 Then addOn wh + 1
End If
ns = Left(ns, wh - 1)
digtot = digtot - newdig
Next
End Sub
Function prmdiv(num)
Dim n, dv, q
If num = 1 Then prmdiv = 1: Exit Function
n = Abs(num): If n > 0 Then limit = Sqr(n) Else limit = 0
If limit <> Int(limit) Then limit = Int(limit + 1)
dv = 2: GoSub DivideIt
dv = 3: GoSub DivideIt
dv = 5: GoSub DivideIt
dv = 7
Do Until dv > limit
GoSub DivideIt: dv = dv + 4 '11
GoSub DivideIt: dv = dv + 2 '13
GoSub DivideIt: dv = dv + 4 '17
GoSub DivideIt: dv = dv + 2 '19
GoSub DivideIt: dv = dv + 4 '23
GoSub DivideIt: dv = dv + 6 '29
GoSub DivideIt: dv = dv + 2 '31
GoSub DivideIt: dv = dv + 6 '37
Loop
If n > 1 Then prmdiv = n
Exit Function
DivideIt:
Do
q = Int(n / dv)
If q * dv = n And n > 0 Then
prmdiv = dv: Exit Function
Else
Exit Do
End If
Loop
Return
End Function
which produces numbers in lexicographic order (1112000111 comes before 20101 as 1 is less than 2).
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Posted by Charlie
on 2015-05-04 19:22:39 |
computer solution