Block #277,174

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 11:33:47 AM · Difficulty 9.9654 · 6,535,721 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

df017194a306c9e2c730fd4216bd91230b1aec8b49d51846c2e4ba004d3baf1e

View on Chainz ↗

Height

#277,174

Difficulty

9.965443

Transactions

Size

2.05 KB

Version

Bits

09f7274b

Nonce

116,782

Timestamp

11/27/2013, 11:33:47 AM

Confirmations

6,535,721

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

94d780380106e83d4407805a9c71b01826c456ba0421b83211e0be160e50c735

Transactions (3)

Coinbase40943a89afa998…4bd992193f0b2f

1 in → 1 out10.0800 XPM110 B

AeKNrjNj…1NEq95Ta

981c8dddc84f33…3a935ec8083479

11 in → 1 out20.3332 XPM1.63 KB

ATsGimmm…XWTWknF1

0652c6be104c6b…680da2daf14c66

1 in → 2 out179.1900 XPM226 B

AHEB8hmZ…NTQbN7Pt AJD1x71H…ZAg9c3Ya

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.

2.634 × 10⁹⁷(98-digit number)

26349485811547643432…14701222778552565759

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

2.634 × 10⁹⁷(98-digit number)

26349485811547643432…14701222778552565759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.634 × 10⁹⁷(98-digit number)

26349485811547643432…14701222778552565761

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

5.269 × 10⁹⁷(98-digit number)

52698971623095286865…29402445557105131519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.269 × 10⁹⁷(98-digit number)

52698971623095286865…29402445557105131521

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

1.053 × 10⁹⁸(99-digit number)

10539794324619057373…58804891114210263039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.053 × 10⁹⁸(99-digit number)

10539794324619057373…58804891114210263041

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

2.107 × 10⁹⁸(99-digit number)

21079588649238114746…17609782228420526079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.107 × 10⁹⁸(99-digit number)

21079588649238114746…17609782228420526081

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

4.215 × 10⁹⁸(99-digit number)

42159177298476229492…35219564456841052159

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 #277,174

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