Unbroken Links of Church
There are religionists who claim they can trace the church from Acts 2 (the inception) down to the present day. They insist there are no interruptions in her history. The Landmark Baptists have made such a claim. "There is a direct, historic 'succession' of Baptist Churches back to New Testament times; true Baptist churches have existed in every century" Handbook of Denominations in the United States, Fourth Edition, pg. 47, by Frank S. Mead). The truth is you can not find any reference to the Baptist Church, as such, until about the fifteenth Century BC.
The odd thing is those who typically make such a boast evidence they do not have an accurate understanding of what the church Jesus built actually was, her nature, function, government, etc. in view of the perverted and scripturally incompatible "church" they advance and practice (the New Testament knows nothing of the Baptist religion, in name, concept or practice).
The church was prophesied. Isaiah prophesied that in the last days the Lord's house would be established. He said it would be established "in the top of the mountains" and "all nations shall flow unto it." He also prophesied that "out of Zion shall go forth the law" (Isa. 2: 2, 3). The "last days" were present in Acts 2 (vs. 17), Paul spoke of the church being the "house of God" and as being in existence (I Tim. 3: 15). Moreover, Jerusalem ("Zion," where the church was begun, Acts 2) was literally located on top of the mountains, and the Jew and Gentile had entrance (Eph. 2: 15-19). The law actually went forth from Jerusalem (Lk. 24: 47-49).
The Lord's church can be identified and duplicated today. A careful study of Acts and the epistles reveal essential traits of the early church. She was established by the Lord (Acts 20: 28, Matt. 16: 18), she taught only the gospel (no creeds, etc., I Tim. 3: 15, Gal. 1: 6-10), she taught belief, repentance, confession of Jesus' deity, and water baptism for the remission of sin as requirements for primary salvation (Acts 2: 36, 8: 37), she was not a denomination (I Cor. 1; 3), each local church was autonomous (Acts 14: 23, I Pet. 5: 2), and she was designated by terms which glorified God, not some man, religion, or movement (cf. Rom. 16: 16). The early church also regularly partook of the Lord's Supper on the Lord's Day (Acts 2: 42, 20: 7).
I personally cannot prove from history that the Lord's church has continued without interruption. However, we can have the true church today simply by being what they were and doing what they did. The "seed of the kingdom" (the word of God, Lk. 8: 11) that produced pristine Christianity in the First Century will produce unadulterated Christianity today - when sown in its purity!