Block #397,939

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/10/2014, 10:00:41 AM · Difficulty 10.4190 · 6,411,510 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d24cf12cb583c3ccbaa584be6960e2faa6d3e8306145308a3f9481f8ad317b0b

View on Chainz ↗

Height

#397,939

Difficulty

10.419037

Transactions

Size

1004 B

Version

Bits

0a6b4604

Nonce

33,883

Timestamp

2/10/2014, 10:00:41 AM

Confirmations

6,411,510

Mined by

⛏️ saRbgAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

5b29ccad16ff9a16c12304df13e4a1e28a02d391f0aee4837cff566ee5e2192f

Transactions (1)

Coinbase5b29ccad16ff9a…ff566ee5e2192f

1 in → 25 out9.1955 XPM913 B

AQvZBsUo…hppgRZTJ AGKhfQo2…h7fBXLX6 Aac9Hjdg…P4ktypc3 ALqxX1WA…hsKjbnXn AZV4TwxQ…8JnQqSoH

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.

2.728 × 10⁹⁷(98-digit number)

27284176231935277443…43318527188100167679

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

2.728 × 10⁹⁷(98-digit number)

27284176231935277443…43318527188100167679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.728 × 10⁹⁷(98-digit number)

27284176231935277443…43318527188100167681

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

5.456 × 10⁹⁷(98-digit number)

54568352463870554887…86637054376200335359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.456 × 10⁹⁷(98-digit number)

54568352463870554887…86637054376200335361

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

1.091 × 10⁹⁸(99-digit number)

10913670492774110977…73274108752400670719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.091 × 10⁹⁸(99-digit number)

10913670492774110977…73274108752400670721

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

2.182 × 10⁹⁸(99-digit number)

21827340985548221954…46548217504801341439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.182 × 10⁹⁸(99-digit number)

21827340985548221954…46548217504801341441

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

4.365 × 10⁹⁸(99-digit number)

43654681971096443909…93096435009602682879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.365 × 10⁹⁸(99-digit number)

43654681971096443909…93096435009602682881

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 #397,939

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