# 421538917598915629

This number is a prime.

42153891 7598915629

The largest known prime factor in "The Octopus" (as of February 3, 2010). It occurs as a(16) in the 7R arm:

2R

```                                                         2=a(1)
22=a(2)
222=a(3)
6222=a(4)
96222=a(5)
9396222=a(6)
6279396222=a(7)
12546279396222=a(8)
148212546279396222=a(9)
300148212546279396222=a(10)
18333300148212546279396222=a(11)
3795318333300148212546279396222=a(12)
1520433795318333300148212546279396222=a(13)
5055121520433795318333300148212546279396222=a(14)
49840565055121520433795318333300148212546279396222=a(15)
2623287849840565055121520433795318333300148212546279396222=a(16)
?=a(17)
```
Let a(1)=2. a(n) is the smallest number > a(n-1) containing a(n-1) as rightmost digits and having exactly n distinct prime factors.

Can you find the next term?
```Honaker: a(1)-a(4)
Gupta: a(5)-a(14)
Andersen: a(15)-a(16)
```
2L
``` a(1)=2
a(2)=21
a(3)=2109
a(4)=21098
a(5)=2109822
a(6)=2109822078
a(7)=2109822078054
a(8)=2109822078054306
a(9)=2109822078054306590
a(10)=21098220780543065904030
a(11)=2109822078054306590403010890
a(12)=210982207805430659040301089001530
a(13)=21098220780543065904030108900153044430
a(14)=?
```
Let a(1)=2. a(n) is the smallest number > a(n-1) containing a(n-1) as leftmost digits and having exactly n distinct prime factors.

Can you find the next term?
```Honaker: a(1)-a(4)
Gupta: a(5)-a(13)
```
3R
```                                                                3=a(1)
33=a(2)
1533=a(3)
491533=a(4)
112491533=a(5)
319112491533=a(6)
393319112491533=a(7)
964393319112491533=a(8)
15905964393319112491533=a(9)
598515905964393319112491533=a(10)
16359598515905964393319112491533=a(11)
2217916359598515905964393319112491533=a(12)
3026852217916359598515905964393319112491533=a(13)
11875083026852217916359598515905964393319112491533=a(14)
340161911875083026852217916359598515905964393319112491533=a(15)
73778782340161911875083026852217916359598515905964393319112491533=a(16)
?=a(17)
```
Let a(1)=3. a(n) is the smallest number > a(n-1) containing a(n-1) as rightmost digits and having exactly n distinct prime factors.

Can you find the next term?
```Honaker: a(1)-a(4)
Gupta: a(5)-a(13)
Andersen: a(14)-a(16)
```
3L
``` a(1)=3
a(2)=33
a(3)=3302
a(4)=33022
a(5)=3302222
a(6)=330222230
a(7)=330222230030
a(8)=330222230030055
a(9)=330222230030055935
a(10)=3302222300300559358065
a(11)=330222230030055935806507470
a(12)=33022223003005593580650747061518
a(13)=33022223003005593580650747061518135430
a(14)=?
```
Let a(1)=3. a(n) is the smallest number > a(n-1) containing a(n-1) as leftmost digits and having exactly n distinct prime factors.

Can you find the next term?
```Honaker: a(1)-a(4)
Gupta: a(5)-a(13)
```
5R
```                                                        5=a(1)
15=a(2)
615=a(3)
18615=a(4)
5718615=a(5)
1055718615=a(6)
1291055718615=a(7)
911291055718615=a(8)
3333911291055718615=a(9)
2183333911291055718615=a(10)
177872183333911291055718615=a(11)
51415177872183333911291055718615=a(12)
1293551415177872183333911291055718615=a(13)
2250601293551415177872183333911291055718615=a(14)
74586822250601293551415177872183333911291055718615=a(15)
574883974586822250601293551415177872183333911291055718615=a(16)
?=a(17)
```
Let a(1)=5. a(n) is the smallest number > a(n-1) containing a(n-1) as rightmost digits and having exactly n distinct prime factors.

Can you find the next term?
```Honaker: a(1)-a(4)
Gupta: a(5)-a(14)
Andersen: a(15), a(16)
```
5L
``` a(1)=5
a(2)=51
a(3)=518
a(4)=5187
a(5)=518738
a(6)=518738066
a(7)=518738066022
a(8)=518738066022891
a(9)=5187380660228910138
a(10)=51873806602289101381770
a(11)=5187380660228910138177036634
a(12)=51873806602289101381770366340485
a(13)=51873806602289101381770366340485096495
a(14)=?
```
Let a(1)=5. a(n) is the smallest number > a(n-1) containing a(n-1) as leftmost digits and having exactly n distinct prime factors.

Can you find the next term?
```Honaker: a(1)-a(4)
Gupta: a(5)-a(13)
```
7R
```                                                                7=a(1)
57=a(2)
357=a(3)
51357=a(4)
3451357=a(5)
1193451357=a(6)
6391193451357=a(7)
20466391193451357=a(8)
699320466391193451357=a(9)
20508699320466391193451357=a(10)
3802320508699320466391193451357=a(11)
5990603802320508699320466391193451357=a(12)
7950455990603802320508699320466391193451357=a(13)
8621077950455990603802320508699320466391193451357=a(14)
108013858621077950455990603802320508699320466391193451357=a(15)
11428690108013858621077950455990603802320508699320466391193451357=a(16)
?=a(17)
```
Let a(1)=7. a(n) is the smallest number > a(n-1) containing a(n-1) as rightmost digits and having exactly n distinct prime factors.

Can you find the next term?
```Honaker: a(1)-a(4)
Gupta: a(5)-a(13)
Andersen: a(14)-a(16)
```
7L
``` a(1)=7
a(2)=74
a(3)=741
a(4)=74102
a(5)=7410255
a(6)=741025545
a(7)=741025545195
a(8)=741025545195705
a(9)=7410255451957051086
a(10)=741025545195705108602109
a(11)=7410255451957051086021092590
a(12)=741025545195705108602109259078965
a(13)=74102554519570510860210925907896578105
a(14)=?
```
Let a(1)=7. a(n) is the smallest number > a(n-1) containing a(n-1) as leftmost digits and having exactly n distinct prime factors.

Can you find the next term?
```Honaker: a(1)-a(4)
Gupta: a(5)-a(13)
```