Block #272,651

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 9:07:52 AM · Difficulty 9.9533 · 6,535,378 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6afc55afeeda4812c2d9a93900dfd0552c7e3547938695e2862a6c5d8eb5e28e

View on Chainz ↗

Height

#272,651

Difficulty

9.953337

Transactions

Size

7.29 KB

Version

Bits

09f40de3

Nonce

187,385

Timestamp

11/25/2013, 9:07:52 AM

Confirmations

6,535,378

Mined by

⛏️ P2SHAGyvY787X6GNhfy8LN8s8Sa6eNshdKQsCK

Merkle Root

01cce58597e4a01e82fdf223d3df49e4f524257d63a2240688b54846f70396f5

Transactions (3)

Coinbase73ff3840267d2c…47dad7c3659691

1 in → 1 out10.1600 XPM109 B

AGyvY787…shdKQsCK

029768606c3ab6…84c41fa37bccd7

2 in → 2 out2008.2305 XPM374 B

APWE6xBz…cg9k96zQ AWjmhp34…Qwzar9Sn

5b6ea395176257…07a2fb1e97c6ba

46 in → 2 out554.0386 XPM6.73 KB

AQvftpUz…fw8JQAtz AdeGjT4s…D1G8qARg

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.

8.802 × 10⁹⁷(98-digit number)

88020144854233608967…30755304614564070399

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

8.802 × 10⁹⁷(98-digit number)

88020144854233608967…30755304614564070399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.802 × 10⁹⁷(98-digit number)

88020144854233608967…30755304614564070401

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

1.760 × 10⁹⁸(99-digit number)

17604028970846721793…61510609229128140799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.760 × 10⁹⁸(99-digit number)

17604028970846721793…61510609229128140801

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

3.520 × 10⁹⁸(99-digit number)

35208057941693443587…23021218458256281599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.520 × 10⁹⁸(99-digit number)

35208057941693443587…23021218458256281601

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

7.041 × 10⁹⁸(99-digit number)

70416115883386887174…46042436916512563199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.041 × 10⁹⁸(99-digit number)

70416115883386887174…46042436916512563201

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

1.408 × 10⁹⁹(100-digit number)

14083223176677377434…92084873833025126399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #272,651

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