Block #385,868

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/2/2014, 2:32:24 AM · Difficulty 10.4038 · 6,441,284 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4f664aa74829dfc618b57197d28d52e38107c014ad1523baeedcdebd0752ab09

View on Chainz ↗

Height

#385,868

Difficulty

10.403792

Transactions

Size

1.90 KB

Version

Bits

0a675ee8

Nonce

141,570

Timestamp

2/2/2014, 2:32:24 AM

Confirmations

6,441,284

Mined by

⛏️ LaRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

642d18222ecf1b48aeb9a9ed9fc0f19739207a1fc2f143f3be2e72cd879e7f20

Transactions (4)

Coinbased7f5a0c0b45fc8…900de8390e218f

1 in → 24 out9.2200 XPM879 B

AQvZBsUo…hppgRZTJ AFutDVqJ…TJTJj6UF Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ATKK7iFz…wZm46KN1

0939b3a469916b…2022b7b9db8017

1 in → 2 out9.1900 XPM225 B

ASw1RBom…FHzGfG3T AeDFWfLr…ocqM5DJT

7d594f814567ab…bbbd757e8fe594

3 in → 2 out9.0952 XPM522 B

AWgpA8GP…eUj4BTG9 ALcFZpaB…J5eU521J

11ccc6065f1db0…46f4f23cf38a4f

1 in → 2 out7.1694 XPM226 B

AN4Kh25c…MNMSoyyd AQmw99is…pF6PqBZM

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.

5.564 × 10⁹⁵(96-digit number)

55647861997257213370…35286783474849402879

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

5.564 × 10⁹⁵(96-digit number)

55647861997257213370…35286783474849402879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.564 × 10⁹⁵(96-digit number)

55647861997257213370…35286783474849402881

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

1.112 × 10⁹⁶(97-digit number)

11129572399451442674…70573566949698805759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.112 × 10⁹⁶(97-digit number)

11129572399451442674…70573566949698805761

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

2.225 × 10⁹⁶(97-digit number)

22259144798902885348…41147133899397611519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.225 × 10⁹⁶(97-digit number)

22259144798902885348…41147133899397611521

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

4.451 × 10⁹⁶(97-digit number)

44518289597805770696…82294267798795223039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.451 × 10⁹⁶(97-digit number)

44518289597805770696…82294267798795223041

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

8.903 × 10⁹⁶(97-digit number)

89036579195611541392…64588535597590446079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.903 × 10⁹⁶(97-digit number)

89036579195611541392…64588535597590446081

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 #385,868

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