Block #397,661

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/10/2014, 6:07:49 AM · Difficulty 10.4145 · 6,404,832 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6c476bf5b5d7160271afc59bc0e50009ea8ac747f21e3eedfeaf5b76c8e1f9b0

View on Chainz ↗

Height

#397,661

Difficulty

10.414460

Transactions

Size

865 B

Version

Bits

0a6a1a11

Nonce

386,513

Timestamp

2/10/2014, 6:07:49 AM

Confirmations

6,404,832

Mined by

⛏️ aRlrAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

99f80f36ebf6df164ad809e36b682899e97e3fe7097aca965e725a9a95cc3eda

Transactions (1)

Coinbase99f80f36ebf6df…725a9a95cc3eda

1 in → 21 out9.2100 XPM777 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AJ8n5XXL…zvZ4TK4P AGKhfQo2…h7fBXLX6

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.

2.004 × 10⁹⁰(91-digit number)

20046263824675255928…95861377101759938199

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

2.004 × 10⁹⁰(91-digit number)

20046263824675255928…95861377101759938199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.004 × 10⁹⁰(91-digit number)

20046263824675255928…95861377101759938201

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

4.009 × 10⁹⁰(91-digit number)

40092527649350511856…91722754203519876399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.009 × 10⁹⁰(91-digit number)

40092527649350511856…91722754203519876401

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

8.018 × 10⁹⁰(91-digit number)

80185055298701023712…83445508407039752799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.018 × 10⁹⁰(91-digit number)

80185055298701023712…83445508407039752801

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

1.603 × 10⁹¹(92-digit number)

16037011059740204742…66891016814079505599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.603 × 10⁹¹(92-digit number)

16037011059740204742…66891016814079505601

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

3.207 × 10⁹¹(92-digit number)

32074022119480409484…33782033628159011199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.207 × 10⁹¹(92-digit number)

32074022119480409484…33782033628159011201

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