Block #276,444

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 4:38:56 AM · Difficulty 9.9632 · 6,541,420 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bcbd4dee336570d5a221c4db03cae3f54e941bf33adf0f190c1134c2a37a895d

View on Chainz ↗

Height

#276,444

Difficulty

9.963188

Transactions

Size

1.08 KB

Version

Bits

09f69382

Nonce

30,334

Timestamp

11/27/2013, 4:38:56 AM

Confirmations

6,541,420

Mined by

⛏️ P2SHAWQ3mouGbYquwYE2vprTzb1jVNHp6Pb56R

Merkle Root

31a1bdba269e7bd0837911cfa6757f28408ff69449c40351cbb6f3853d1ce03e

Transactions (5)

Coinbasef782dc51577941…40c53735caf6f6

1 in → 1 out10.1000 XPM109 B

AWQ3mouG…Hp6Pb56R

e0f25055fafdbf…e2297e7791d9d0

1 in → 2 out2.8900 XPM225 B

AND32a6K…m333QUDV AXvHJWgZ…jnog9Qug

ef6b6acfaa3c8c…8c4f84fe8e6d8f

1 in → 2 out48.6582 XPM226 B

AWFgLn8c…sVdeRB6s AVKF9xiF…KvqgN9Tc

ed45805452c5ad…72de5367715896

1 in → 2 out8.0187 XPM226 B

ARAWJCHA…xuYpFzcw AcLDvygp…GAR414Po

332b5fb6532d36…c10e033ebe0361

1 in → 2 out6.9322 XPM226 B

AXSGgyCR…YigWjfpz AMQbf34W…gfbBrPGD

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.

7.633 × 10⁹¹(92-digit number)

76333822506362975964…88912777024466657279

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

7.633 × 10⁹¹(92-digit number)

76333822506362975964…88912777024466657279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.633 × 10⁹¹(92-digit number)

76333822506362975964…88912777024466657281

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

1.526 × 10⁹²(93-digit number)

15266764501272595192…77825554048933314559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.526 × 10⁹²(93-digit number)

15266764501272595192…77825554048933314561

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

3.053 × 10⁹²(93-digit number)

30533529002545190385…55651108097866629119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.053 × 10⁹²(93-digit number)

30533529002545190385…55651108097866629121

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

6.106 × 10⁹²(93-digit number)

61067058005090380771…11302216195733258239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.106 × 10⁹²(93-digit number)

61067058005090380771…11302216195733258241

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

1.221 × 10⁹³(94-digit number)

12213411601018076154…22604432391466516479

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 #276,444

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