Adám
# [APL (Dyalog Extended)], 12 [bytes](https://codegolf.meta.stackexchange.com/a/9429/43319 "When can APL characters be counted as 1 byte each?") ([SBCS](https://github.com/abrudz/SBCS ".dyalog files using a single byte character set"))
Anonymous tacit prefix function
```apl
+/1⍭10⊥¨2,/⊢
```
[Try it online!][TIO-k88nntu1]
`⊢` the argument
`2,/` pair-wise concatenation
`10⊥¨` evaluate each as base-10
`1⍭` indicate the primes
`+/` sum
[APL (Dyalog Extended)]: https://github.com/abrudz/dyalog-apl-extended
[TIO-k88nntu1]: https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/X1vf8FHvWkODR11LD60w0tF/1LXof9qjtgmPevsedTU/6l3zqHfLofXGj9omPuqbGhzkDCRDPDyD/6cpmCkYKlgqmCsYA7EhkDQEQnMFS640MN9QwQgsawjmWwDlTYC0CZgPkgOxTYFmGANVWQAA "APL (Dyalog Extended) – Try It Online"

Answer #2

xigoi
# [Jelly], 6 bytes
D,ƝḌẒS
[Try it online!][TIO-khpch540]
[Jelly]: https://github.com/DennisMitchell/jelly
[TIO-khpch540]: https://tio.run/##y0rNyan8/99F59jchzt6Hu6aFPz//39zC2MTcxNDAA "Jelly – Try It Online"
## Explanation
D,ƝḌẒS Main monadic link
D Decimal digits
Ɲ For each pair of neighboring elements:
, Pair
Ḍ Number from decimal digits [each]
Ẓ Is prime?
S Sum