A059496 is finite with last term a(114) = 149.

We have to show:
1) a(114) = 149
2) 149 has no new prime successor,
   that is we get only composites or already occurring primes,
   when prepending or replacing any digit by a nonzero digit.

We omit (1), and for (2) we have only to inspect the following
complete list of candidate successors of 149.


                    {140 + d | d = 1 .. 9}
141 = 3 * 47
142 = 2 * 71
143 = 11 * 13
144 = 2^4 * 3^2
145 = 5 * 29
146 = 2 * 73
147 = 3 * 7^2
148 = 2^2 * 37
149 = a(114)

                    {109 + 10*d | d = 1 .. 9}
119 = 7 * 17
129 = 3 * 43
139 = a(23)
149 = a(114)
159 = 3 * 53
169 = 13^2
179 = a(113)
189 = 3^3 * 7
199 = a(22)

                    {49 + 100*d | d = 1 .. 9}
149 = a(114)
249 = 3 * 83
349 = a(85)
449 = a(93)
549 = 3^2 * 61
649 = 11 * 59
749 = 7 * 107
849 = 3 * 283
949 = 13 * 73

                    {149 + 1000*d | d = 1 .. 9}
1149 = 3 * 383
2149 = 7 * 307
3149 = 47 * 67
4149 = 3^2 * 461
5149 = 19 * 271
6149 = 11 * 13 * 43
7149 = 3 * 2383
8149 = 29 * 281
9149 = 7 * 1307

.

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reinhard.zumkeller@gmail.com, Jan 6 2014