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In parshat chukat it says that if you become tamei due to a dead body, you become pure again by being sprinkled with red-heifer ash-water on the third and seventh day of your impurity, but if you don't then you remain impure... 12 the same shall purify himself therewith on the third day and on the seventh day, and he shall be clean; but if he purify not himself the third day and the seventh day, he shall not be clean. יג כָּל-הַנֹּגֵעַ בְּמֵת בְּנֶפֶשׁ הָאָדָם אֲשֶׁר-יָמוּת וְלֹא יִתְחַטָּא, אֶת-מִשְׁכַּן יְהוָה טִמֵּא--וְנִכְרְתָה הַנֶּפֶשׁ הַהִוא, מִיִּשְׂרָאֵל: כִּי מֵי נִדָּה לֹא-זֹרַק עָלָיו, טָמֵא יִהְיֶה--עוֹד, טֻמְאָתוֹ בוֹ. 13 Whosoever toucheth the dead, even the body of any man that is dead, and purifieth not himself--he hath defiled the tabernacle of the LORD--that soul shall be cut off from Israel; because the water of sprinkling was not dashed against him, he shall be unclean; his uncleanness is yet upon him.

So what happens if you miss days 3 and 7 of the sprinkling (either intentionally or on purpose). Are you tamei forever?

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if you miss days 3 and 7 ... are you tamei forever?

No. you need to count 3 days 3 to begin, the rule is to begin when you go to Cohen. this may by at day day 4, 5... So day(2nd sprinkling) >= day(1st sprinkling) + 4

Rambam Mishne Taharot Para Aduma 11, 2

When a person became impure due to a corpse and remained several days without having the water sprinkled upon him, when he comes to have the water sprinkled upon him, he should count three days in our presence. The water is sprinkled upon him on the third and seventh days. He immerses in a mikveh on the seventh day and waits until nightfall.

To whom does the above apply? To a common person who comes to have the water sprinkled upon him. Even if he says that this is the third day after he contracted impurity, his word is not accepted, for perhaps he became impure on this day. Therefore, he must count the days in our presence. If, by contrast, a chaver (which is able to know alone) comes to have the water sprinkled upon him, it may be sprinkled on him and his implements immediately.

When such water was sprinkled on a person on the third day, but it was not sprinkled upon him on the seventh day, he may immerse in a mikveh whenever he desires after the seventh day, whether during the night or during the day and the water should be sprinkled on him during the day, whether before immersion or after immersion. Even if he immersed on the night of the ninth day or the night of the tenth day, the water may be sprinkled on him on the following day after sunrise.

The topic is more complex, with discussions between Rishonim, but for the specific question you ask, the above answer may be sufficient.

See here for further reading

  • For the 2nd springling more than 4 days after the first, it is regular also. I found in Sifre Chukkat, 129:

    ואם לא הזה שביעי, שמיני, תשיעי, עשירי מניין? תלמוד לומר וחיטאו מכל מקום. ‏

  • I solved the secnd part of the question – kouty Jul 18 '16 at 20:34

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