Block #279,737

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 10:57:46 AM · Difficulty 9.9726 · 6,523,157 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b65b359b01bd96b2b0bb6a0fa7f9be4eb97b03eb057986849d06ffe2d1866a8a

View on Chainz ↗

Height

#279,737

Difficulty

9.972631

Transactions

Size

1.20 KB

Version

Bits

09f8fe54

Nonce

9,213

Timestamp

11/28/2013, 10:57:46 AM

Confirmations

6,523,157

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

1ba40779472da721e81a8173460814fc48353879a6acd0e051165f14edfff500

Transactions (3)

Coinbase3865a38b6ebe5c…bd0ac0b82ac757

1 in → 1 out10.0600 XPM109 B

AeKNrjNj…1NEq95Ta

358e7a919c4fea…030e3cdc0c86ba

3 in → 9 out30.1900 XPM658 B

AeKNrjNj…1NEq95Ta AKL6bdQp…hNjj8m2T AYJq4YVd…sPb3dC2v AdS1bhZG…1xodpY3J AcADmAoe…8iNnoMzB

80e2e95309e8e0…bd1712f2ccb596

2 in → 2 out10.5843 XPM374 B

AU8c2HE2…KCz3EuwC APUSXf5S…vcZ72ki2

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.

3.388 × 10⁹⁴(95-digit number)

33880421231864122860…32915251107035997599

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

3.388 × 10⁹⁴(95-digit number)

33880421231864122860…32915251107035997599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.388 × 10⁹⁴(95-digit number)

33880421231864122860…32915251107035997601

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

6.776 × 10⁹⁴(95-digit number)

67760842463728245721…65830502214071995199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.776 × 10⁹⁴(95-digit number)

67760842463728245721…65830502214071995201

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

1.355 × 10⁹⁵(96-digit number)

13552168492745649144…31661004428143990399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.355 × 10⁹⁵(96-digit number)

13552168492745649144…31661004428143990401

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

2.710 × 10⁹⁵(96-digit number)

27104336985491298288…63322008856287980799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.710 × 10⁹⁵(96-digit number)

27104336985491298288…63322008856287980801

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

5.420 × 10⁹⁵(96-digit number)

54208673970982596577…26644017712575961599

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