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Lord Rama Appeared 17.7 million years ago
By BRS Swami Gaurangapada

Shrila Rupa Goswami's Laghu Bhagavatamrta Text 78:

kausalyayam dasarathan

nava-durva dala-dyutih

tretayam avirabhavac

caturvimse catur-yuge

bharatena sumitraya

nandanabhyam ca samyutah

kausalyayam-in the womb of Kausalya-devi; dasarathat-from Dasaratha Maharaja; nava-fresh; durva-dala-durva grass; dyutiH-with the splendor; tretayam-during the Treta-yuga; avirabhavat-appeared; caturvimse-during the 24th; catuh-yuge-cycle of four yugas; bharatena-by Bharata; sumitrayaH-of Sumitra; nandanabhyam-by the two sons (Laksmana and Satrughna); ca-also; samyutaH-accompanied.

"Splendid as a new blade of durva grass, and accompanied by Sumitra's two sons and by Bharata, Lord Ramachandra appeared in the Treta-yuga of the 24th catur-yuga as the son of Kausalya and Dasaratha."

[It is clearly mentioned that caturvimse catur yuge i.e during the 24th caturyuga. Calculations: 1 Catur-yuga= 4,320,000 years or 43 lakh 20 thousand years]

Catur-yugas passed = 24th part (roughly half) of Treta & full Kali, 25th, 26th, 27th, 28th till part of Kali-yuga.

Years passed approx. = 432,000 + 432,000 + 4,320,000 + 4,320,000 + 4,320,000 + (4,320,000-427,000 left)

= 17,717,000 (+or-432,000 years)

(+ or - 432,000 years is required because we don't exactly know in which period of Treta Yuga of the 24th Chatur-yuga Lord Rama appeared, He appeared).

This is a most beautiful & detailed narration about the appearance of Lord Ramachandra from the book (Valmiki) "Ramayana" by Shriman Purnaprajna dasa.