In Śrīmad-Bhāgavatam there is the following statement regarding Śrī Caitanya Mahāprabhu:
kṛṣṇa-varṇaṁ tviṣākṛṣṇaṁ
sāṅgopāṅgāstra-pārṣadam
yajñaiḥ saṅkīrtana-prāyair
yajanti hi su-medhasaḥ
yajñaiḥ saṅkīrtana-prāyair
yajanti hi su-medhasaḥ
“In the Age of Kali, people who are endowed with sufficient intelligence will worship the Lord, who is accompanied by His associates, by performance of saṅkīrtana-yajña.” (Bhāg.11.5.32) Śrī Caitanya Mahāprabhu is always accompanied by His plenary expansion Śrī Nityānanda Prabhu, His incarnation Śrī Advaita Prabhu, His internal potency Śrī Gadādhara Prabhu and His marginal potency Śrīvāsa Prabhu. He is in the midst of them as the Supreme Personality of Godhead. One should know that Śrī Caitanya Mahāprabhu is always accompanied by these other tattvas. Therefore our obeisances to Śrī Caitanya Mahāprabhu are complete when we say śrī-kṛṣṇa-caitanya prabhu -ityānanda śrī-advaitagadādhara śrīvāsādi-gaura-bhakta-vṛnda. As preachers of the Kṛṣṇa consciousness movement, we first offer our obeisances to Śrī Caitanya Mahāprabhu by chanting this Pañca–tattva mantra; then we say Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare HareRāma, Hare Rāma, Rāma Rāma, Hare Hare. There are ten offenses in the chanting of the Hare Kṛṣṇa mahā-mantra, but these are not considered in the chanting of the Pañca–tattvamantra, namely, śrī-kṛṣṇa-caitanya prabhu-nityānanda śrī-advaita gadādharaśrīvāsādi-gaura-bhakta-vṛnda. Śrī Caitanya Mahāprabhu is known as mahā-vadānyāvatāra, the most magnanimous incarnation, for He does not consider the offenses of the fallen souls. Thus to derive the full benefit of the chanting of the mahā-mantra(Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare), we must first take shelter of Śrī Caitanya Mahāprabhu, learn the Pañca–tattvamahā-mantra, and then chant the Hare Kṛṣṇa mahā-mantra. That will be very effective.
Taking advantage of Śrī Caitanya Mahāprabhu, many unscrupulous devotees manufacture a mahā-mantra of their own. Sometimes they sing, bhaja nitāi gaura rādheśyāma hare kṛṣṇa hare rāma or śrī-kṛṣṇa-caitanya prabhu-nityānanda hare kṛṣṇa harerāma śrī-rādhe govinda. Actually, however, one should chant the names of the full Pañca–tattva (śrī-kṛṣṇa-caitanya prabhu-nityānanda śrī-advaita gadādhara śrīvāsādi-gaura-bhakta-vṛnda) and then the sixteen words Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, HareHare Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare, but these unscrupulous, less intelligent men confuse the entire process. Of course, since they are also devotees they can express their feelings in that way, but the method prescribed by Śrī Caitanya Mahāprabhu’s pure devotees is to chant first the full Pañca–tattva mantra and then chant the mahā-mantra–Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare Hare Rāma, Hare Rāma, RāmaRāma, Hare Hare.
Śrī Caitanya-caritāmṛta Ādi-līlā 7.4 – Purport
His Divine Grace A.C. Bhaktivedanta Swami Prabhupāda

The authentic account of Lord Caitanya Mahāprabhu’s pastimes and teachings, revealing His mission to spread the purest form of devotional service to Krishna through the chanting of His holy names.