Block #384,318

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/1/2014, 12:50:04 AM · Difficulty 10.4023 · 6,422,063 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e7c1578af70f1a1b45ef2204cd2f514936d8d56a0a52b69028de95dd7ee8658b

View on Chainz ↗

Height

#384,318

Difficulty

10.402317

Transactions

Size

1.05 KB

Version

Bits

0a66fe47

Nonce

150,546

Timestamp

2/1/2014, 12:50:04 AM

Confirmations

6,422,063

Mined by

⛏️ >aRDaAFutDVqJywBDvDDzwUNgUinUiETJTJj6UF

Merkle Root

b798c6ef732cb855d1072422a30dd7e820939eb63b4dc8e59cfc1b37da8fd8d2

Transactions (1)

Coinbaseb798c6ef732cb8…fc1b37da8fd8d2

1 in → 27 out9.2300 XPM981 B

AFutDVqJ…TJTJj6UF AGKhfQo2…h7fBXLX6 ATKK7iFz…wZm46KN1 AXX1wTMN…FfSE8V61 AN6KvTCW…8tVTJUpq

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.

3.781 × 10⁹⁷(98-digit number)

37810848820260982782…99578353025759247359

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

3.781 × 10⁹⁷(98-digit number)

37810848820260982782…99578353025759247359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.781 × 10⁹⁷(98-digit number)

37810848820260982782…99578353025759247361

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

7.562 × 10⁹⁷(98-digit number)

75621697640521965565…99156706051518494719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.562 × 10⁹⁷(98-digit number)

75621697640521965565…99156706051518494721

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

1.512 × 10⁹⁸(99-digit number)

15124339528104393113…98313412103036989439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.512 × 10⁹⁸(99-digit number)

15124339528104393113…98313412103036989441

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

3.024 × 10⁹⁸(99-digit number)

30248679056208786226…96626824206073978879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.024 × 10⁹⁸(99-digit number)

30248679056208786226…96626824206073978881

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

6.049 × 10⁹⁸(99-digit number)

60497358112417572452…93253648412147957759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.049 × 10⁹⁸(99-digit number)

60497358112417572452…93253648412147957761

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 #384,318

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