buddy i also faced the same problem. i waited for ue4 to verify nearly 1 hrs. but finally found a solution for our problem. it happens becoz when ur anti-virus is turned on with live protection. here is the solution for ur problem:
1]pause the download
2] turn off ur anti-virus
3] now resume ur download
now ur ue4 will start to verifying…
this problem cause becoz ur anti-virus wont allow any software to read or check ur file unless u get permission from administrator.