Block #538,937

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/12/2014, 12:57:35 PM · Difficulty 10.9247 · 6,271,318 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1f10c22593e5a83e324501529aec4860a316d51632d317fab69a164f22f0d001

View on Chainz ↗

Height

#538,937

Difficulty

10.924701

Transactions

Size

427 B

Version

Bits

0aecb932

Nonce

283,120,328

Timestamp

5/12/2014, 12:57:35 PM

Confirmations

6,271,318

Mined by

⛏️ P2SHAMQW2ZX3UpCedDN2eEwVyVJFS7iDXgjQmE

Merkle Root

5cfd702d068d63f24943a57570b53e654d763efecd71ee13430bf41bf636d0d9

Transactions (2)

Coinbase3706220f64b359…18208aa5cdd20b

1 in → 1 out8.3800 XPM109 B

AMQW2ZX3…iDXgjQmE

d70a063a8aca5a…1d6db7dbf57c65

1 in → 3 out8.3900 XPM227 B

ALHh4KEC…iRJuWFy8 AeKNrjNj…1NEq95Ta AHXJ1dhk…mhL46N6m

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.

7.692 × 10⁹⁶(97-digit number)

76923853499419675268…15501795022296411039

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

7.692 × 10⁹⁶(97-digit number)

76923853499419675268…15501795022296411039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.692 × 10⁹⁶(97-digit number)

76923853499419675268…15501795022296411041

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

1.538 × 10⁹⁷(98-digit number)

15384770699883935053…31003590044592822079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.538 × 10⁹⁷(98-digit number)

15384770699883935053…31003590044592822081

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

3.076 × 10⁹⁷(98-digit number)

30769541399767870107…62007180089185644159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.076 × 10⁹⁷(98-digit number)

30769541399767870107…62007180089185644161

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

6.153 × 10⁹⁷(98-digit number)

61539082799535740214…24014360178371288319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.153 × 10⁹⁷(98-digit number)

61539082799535740214…24014360178371288321

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

1.230 × 10⁹⁸(99-digit number)

12307816559907148042…48028720356742576639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.230 × 10⁹⁸(99-digit number)

12307816559907148042…48028720356742576641

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 #538,937

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