Ron Guth:
Proof 1834 Half Dimes are extremely rare. Experts have argued over the number of survivors, but it appears that there are at least twenty demonstrably different examples and perhaps as many as thirty. When Breen wrote his Encyclopedia of United States Proof Coins in 1977, he was "fairly sure" that he knew of fifteen different specimens, but by 1988 he had raised the number to twenty Proofs. We have positively identified at least fifteen different examples, with the possibility of a few more examples out there, but it is unlikely that there are more than twenty.
Most Proof 1834 Half Dimes are of the LM-4 variety. Logan and McCloskey cite a single LM-1 variety in Proof, but the last time that coin appeared on the market was in 1991. Many of the known Proofs have one or more lintmarks, which are common on Proofs, but not on coins made for circulation. Cameo examples are exceedingly rare and only a single example is known. PR66 seems to be the top grade for this issue.