Block #402,354

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/13/2014, 9:36:30 AM · Difficulty 10.4350 · 6,396,978 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

851e8ca50c08ef838b658f32a7f4b92187f7c75f76c4be0be1720a49b71378a5

View on Chainz ↗

Height

#402,354

Difficulty

10.435038

Transactions

Size

1.06 KB

Version

Bits

0a6f5ea7

Nonce

92,847

Timestamp

2/13/2014, 9:36:30 AM

Confirmations

6,396,978

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

568f593a42f360b9751b8a5958147f6773b9b596b06cb33888e0c566c950715f

Transactions (2)

Coinbase0ad6d31072e770…c0dc239e1e304b

1 in → 1 out9.1800 XPM116 B

AbwWkWZt…kawDhufa

d2c10b8b779e3f…56c32a1dca883d

4 in → 12 out36.8200 XPM873 B

AaDoMwC4…cXYC9cEm AeFZ6Pga…8BcMXJU1 AVHrLth7…2B2Ly7Fc AQpF1vAG…Zo8pfzv2 AeKNrjNj…1NEq95Ta

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.

2.550 × 10⁹⁹(100-digit number)

25506614756425871177…35603380927195955199

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

2.550 × 10⁹⁹(100-digit number)

25506614756425871177…35603380927195955199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.550 × 10⁹⁹(100-digit number)

25506614756425871177…35603380927195955201

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

5.101 × 10⁹⁹(100-digit number)

51013229512851742354…71206761854391910399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.101 × 10⁹⁹(100-digit number)

51013229512851742354…71206761854391910401

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

1.020 × 10¹⁰⁰(101-digit number)

10202645902570348470…42413523708783820799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.020 × 10¹⁰⁰(101-digit number)

10202645902570348470…42413523708783820801

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

2.040 × 10¹⁰⁰(101-digit number)

20405291805140696941…84827047417567641599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.040 × 10¹⁰⁰(101-digit number)

20405291805140696941…84827047417567641601

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

4.081 × 10¹⁰⁰(101-digit number)

40810583610281393883…69654094835135283199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.081 × 10¹⁰⁰(101-digit number)

40810583610281393883…69654094835135283201

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