Block #276,562

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 5:47:20 AM · Difficulty 9.9635 · 6,533,335 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e154b5c7c75d446feca1b686c48898563564321cd82f288e136805cb3903cb15

View on Chainz ↗

Height

#276,562

Difficulty

9.963534

Transactions

Size

1.51 KB

Version

Bits

09f6aa2c

Nonce

62,300

Timestamp

11/27/2013, 5:47:20 AM

Confirmations

6,533,335

Mined by

⛏️ R8aRAbv8pzf1A44ES9RdtZpBP4z1zat4zPXDTV

Merkle Root

f153f6e4883ef602713bbedfb4c4eed9ccf3bcdb7254182e01744224c80c4b9a

Transactions (2)

Coinbaseda261565e826e4…f77d89f763f36d

1 in → 30 out10.0400 XPM1.06 KB

Abv8pzf1…t4zPXDTV AaZptiTm…mxymWwAJ AbiApRgN…g8QuFUwL ANkX1YyE…kHwVW1hd Aai6TNLM…kQf2QbQd

72578800e3e764…c8126823d34467

2 in → 2 out5.0254 XPM374 B

AMhdLHbY…6FS66kj2 AckRtPy6…b1c9pvPK

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.

2.534 × 10⁹³(94-digit number)

25341079623938347999…34183376148155658879

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

2.534 × 10⁹³(94-digit number)

25341079623938347999…34183376148155658879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.534 × 10⁹³(94-digit number)

25341079623938347999…34183376148155658881

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

5.068 × 10⁹³(94-digit number)

50682159247876695998…68366752296311317759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.068 × 10⁹³(94-digit number)

50682159247876695998…68366752296311317761

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

1.013 × 10⁹⁴(95-digit number)

10136431849575339199…36733504592622635519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.013 × 10⁹⁴(95-digit number)

10136431849575339199…36733504592622635521

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

2.027 × 10⁹⁴(95-digit number)

20272863699150678399…73467009185245271039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.027 × 10⁹⁴(95-digit number)

20272863699150678399…73467009185245271041

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

4.054 × 10⁹⁴(95-digit number)

40545727398301356798…46934018370490542079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.054 × 10⁹⁴(95-digit number)

40545727398301356798…46934018370490542081

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 #276,562

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