Block #1,206,017

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/23/2015, 11:04:30 PM · Difficulty 10.7850 · 5,637,283 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

a9f91c763ff15225d4ebd16e2e8d7ef3dc225f7151ba975164a7cdf718a9a20b

View on Chainz ↗

Height

#1,206,017

Difficulty

10.784965

Transactions

Size

1.01 KB

Version

Bits

0ac8f373

Nonce

101,455,918

Timestamp

8/23/2015, 11:04:30 PM

Confirmations

5,637,283

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

4f2188c2cac3c0b11a347abc1f859343cc4d17df56fa5b5ea18a51181221b42d

Transactions (4)

Coinbasea03e77d420ecae…7617b5ceecabbb

1 in → 1 out8.6100 XPM116 B

AJCEY9yy…tg97E6zm

b3a55f8515fb7f…7e3b16e8ce48f9

1 in → 2 out4263.5900 XPM226 B

ANuuNBU8…FHKHmYUs AGAht2CN…6pHKm9M5

916d367166f332…cfa1b38181be1c

1 in → 2 out854.5100 XPM226 B

ARezZb4y…FxP7ivbi AGE71368…wm6d7yhp

332a57aa6e363a…3355e13731bfde

2 in → 2 out2.0300 XPM373 B

AGAPK7tn…xUvQivce ANENp83D…B5oLXppE

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.052 × 10⁹⁸(99-digit number)

20529648627455267731…20227289698723839999

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.052 × 10⁹⁸(99-digit number)

20529648627455267731…20227289698723839999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.052 × 10⁹⁸(99-digit number)

20529648627455267731…20227289698723840001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

4.105 × 10⁹⁸(99-digit number)

41059297254910535463…40454579397447679999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.105 × 10⁹⁸(99-digit number)

41059297254910535463…40454579397447680001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

8.211 × 10⁹⁸(99-digit number)

82118594509821070927…80909158794895359999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.211 × 10⁹⁸(99-digit number)

82118594509821070927…80909158794895360001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.642 × 10⁹⁹(100-digit number)

16423718901964214185…61818317589790719999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.642 × 10⁹⁹(100-digit number)

16423718901964214185…61818317589790720001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.284 × 10⁹⁹(100-digit number)

32847437803928428370…23636635179581439999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.284 × 10⁹⁹(100-digit number)

32847437803928428370…23636635179581440001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #1,206,017

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