Block #437,589

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/10/2014, 9:59:54 AM · Difficulty 10.3578 · 6,376,608 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cccc279e180e328b606e3dc323fda9f2e9c0b14f64b714808c1dc0322d26f01b

View on Chainz ↗

Height

#437,589

Difficulty

10.357801

Transactions

Size

1.83 KB

Version

Bits

0a5b98d4

Nonce

174,564

Timestamp

3/10/2014, 9:59:54 AM

Confirmations

6,376,608

Mined by

⛏️ UaSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

19fbda40a6ece1db9748b26eb7a527a05b91120c0d57860f7836319b0764bca0

Transactions (4)

Coinbase8963c08feb01f2…5ad19ed4d58e0c

1 in → 23 out9.3100 XPM844 B

AQvZBsUo…hppgRZTJ AGD4yZQw…hGzM2XAx Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

09a80477dec3fc…a0fa638a8b4d85

3 in → 1 out7.6900 XPM488 B

AZ27GWsq…eQF8QeNS

7fb3d21a81f554…0e6a84144b7284

1 in → 2 out5.1593 XPM226 B

AZNkVsLP…g6UbMDD9 AYirVUBS…1ivWLbF2

bbca670efde18f…5ed3df71c427b0

1 in → 2 out1.4638 XPM225 B

AVpZxRYx…REyhJEBY ASfQj9Pb…Q87HBF2g

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.

3.156 × 10⁹²(93-digit number)

31560835871699994014…12555217295998480639

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

3.156 × 10⁹²(93-digit number)

31560835871699994014…12555217295998480639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.156 × 10⁹²(93-digit number)

31560835871699994014…12555217295998480641

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

6.312 × 10⁹²(93-digit number)

63121671743399988029…25110434591996961279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.312 × 10⁹²(93-digit number)

63121671743399988029…25110434591996961281

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

1.262 × 10⁹³(94-digit number)

12624334348679997605…50220869183993922559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.262 × 10⁹³(94-digit number)

12624334348679997605…50220869183993922561

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

2.524 × 10⁹³(94-digit number)

25248668697359995211…00441738367987845119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.524 × 10⁹³(94-digit number)

25248668697359995211…00441738367987845121

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

5.049 × 10⁹³(94-digit number)

50497337394719990423…00883476735975690239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.049 × 10⁹³(94-digit number)

50497337394719990423…00883476735975690241

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 #437,589

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