CURLINFO_NUM_CONNECTS man page
CURLINFO_NUM_CONNECTS — get number of created connections
CURLcode curl_easy_getinfo(CURL *handle, CURLINFO_NUM_CONNECTS, long *nump);
Pass a pointer to a long to receive how many new connections libcurl had to create to achieve the previous transfer (only the successful connects are counted). Combined with CURLINFO_REDIRECT_COUNT(3) you are able to know how many times libcurl successfully reused existing connection(s) or not. See the connection options of curl_easy_setopt(3) to see how libcurl tries to make persistent connections to save time.
Added in 7.12.3
Returns CURLE_OK if the option is supported, and CURLE_UNKNOWN_OPTION if not.