Thank you for your help.
I think there was Google Authenticator at that time.
Somehow the 1JvooVJkuEe9bA1grCve2o5DRzkCv2gAB6 address seems to be linked to Coinbase, maybe you forgot you moved the funds ?
How do you know it is Coinbase?
More than 10 years have passed since those transactions happened. It's possible that you forgot about it and can't remember what you did or where you moved your coins. Do you still have access to your Paymium account? If you log in and check your trading and withdrawal activity, do the records match to what Paymium's support agent told you? Besides Paymium, what other services and wallets did you use at the time? That's where I would look in search for the missing funds.
In Paymium, it says: Transaction to an external wallet the same day of the purchase.
But it can be an internal job. There were suspicion about Paymium CTO @davout (ex Bitcoin-Central) at that time. You can read some posts about it here in this forum.
I bought Bitcoin on May 23, 2014, via Paymium at 20:11:30, and it was delivered to this wallet: 19CEZVuiARGq2n1f9rx7ndejgw4RpF8gaY.
However, it seems that the BTC was transferred the same day (May 23, 2014) at 21:22:00 to another wallet: 1JvooVJkuEe9bA1grCve2o5DRzkCv2gAB6.
I noticed paymium support has mentioned your withdrawal request was processed and transferred on May 25th? a mistake? Also, if it's s a custodial exchange, the withdrawal could come from another address then-- not 19CEZ
I hope you still have your old email accounts because you might be able to find hints that way. Try to search every possible keyword you could think of. You may be able to find account/s from other platforms for instance.
I guess May 25th is a mistake, not sure why they mentioned that date. They say that the Transaction was taken into account 2 days after the request. But it is not true.
Can you explain that part "if it's s a custodial exchange, the withdrawal could come from another address then-- not 19CEZ"?
What does it mean?