No. there is more in the prerequisites:
(1) The above is required, but is not enough. More than 500 had seen the risen Lord. Too general.
(2) If you search the Scripture, you will see that a chief apostle had to be one who was called out and chosen by the Lord himself and by the determined will (thelayma) of God. Matthias was not. Paul was. There are no other. Paul is Christ's choice to fill the place of Judas Iscariot.
(3) An apostle is not chosen by other men. Matthias was chosen by men, most particularly by the prodding of the ever-erroring Peter after his conversion but before his spiritual regeneration. Peter dreamed up this scheme, probably to try to assert leadership. But he did not appear to do it under control by the Holy Spirit. It was Peter's will, not God's. Matthias was numbered with the eleven apostles. He was never denominated as an apostle. Matthias, for a while, was counted with "the twelve" but note that the specific title there was not supplied for him by the Holy Scripture. In contrast, Paul was called "apostle" not of (apo) men or by (dia)(a) man, but by Jesus Christ and God The Father. You can not say that any apostle since Christ's ascension other than Paul meets this requirement.
(4) An apostle must also have manifested God working through him by signs, wonders, and mighty deeds. (2 Cor. 12:12) Those are not accomplished today by anyone claiming to fill the apostleship.
(5) If there is an apostle today, where are the other eleven?
Don't be buffaloed by those who hold shaky opinions and try to back it up with reliance on "tradition" and poor hermeneutics, but neglect the unarguable sense of The Word. But you must do your work in the Word to exercise spiritual discernment, otherwise they will overcome you with the natural mind, the "how-many-angels-can-dance-on-the-head-of-a-pin" kind of logic.
It goes on to state that Matthias was numbered with the eleven apostles. If that prayer to the Lord was not enough, and He did not like the choice of Matthias, please show by scripture this belief. It was a nomination prayer, and Matthias was chosen to be numbered with the 11.
Please read Gal. 1:11-24. It will answer the question of Paul's ministry and why he was NEVER to be counted among Peter and the 11. Not even by Christ Himself. Paul's ministry was not the same as the 12.