Block #363,229

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/17/2014, 7:02:26 AM · Difficulty 10.4111 · 6,439,413 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

15db0dbf4e8412b7c07799a5a1f39d88319222ee2717ebdb62e6188a64eddfdb

View on Chainz ↗

Height

#363,229

Difficulty

10.411111

Transactions

Size

1.09 KB

Version

Bits

0a693e8d

Nonce

166,416

Timestamp

1/17/2014, 7:02:26 AM

Confirmations

6,439,413

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

57130b64223f5b4d1c9a5f4375e9a21620df69e7bfa99a0ca877dc3e24147888

Transactions (5)

Coinbase759f8a91ed5a28…3b5296c519dc46

1 in → 1 out9.2500 XPM116 B

AbwWkWZt…kawDhufa

86fde5c43facc2…cee381091177f5

1 in → 2 out8.1264 XPM227 B

AaE4yTG2…kVoRGyoR AdfHhZ6o…6swH6dxw

8bf8ba059f2427…fa2799fd3aa867

1 in → 2 out6.2016 XPM226 B

Ac24WwPt…BSeTbxUj APXjc5TP…HM69AhXp

50306084a48371…7ad6bf0c975b17

1 in → 2 out5.1880 XPM226 B

ANRBY6qw…deuUeef8 AZ95uzmE…aYSVuLXb

ff61a73de5f8cf…2c5a935e5d8bd5

1 in → 2 out5.1995 XPM227 B

ALWdgr9V…6JqUAzU5 AHHmR85y…uEUgHRhd

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.

2.619 × 10⁹⁷(98-digit number)

26197444598108517352…54632236763633123519

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

2.619 × 10⁹⁷(98-digit number)

26197444598108517352…54632236763633123519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.619 × 10⁹⁷(98-digit number)

26197444598108517352…54632236763633123521

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

5.239 × 10⁹⁷(98-digit number)

52394889196217034705…09264473527266247039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.239 × 10⁹⁷(98-digit number)

52394889196217034705…09264473527266247041

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

1.047 × 10⁹⁸(99-digit number)

10478977839243406941…18528947054532494079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.047 × 10⁹⁸(99-digit number)

10478977839243406941…18528947054532494081

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

2.095 × 10⁹⁸(99-digit number)

20957955678486813882…37057894109064988159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.095 × 10⁹⁸(99-digit number)

20957955678486813882…37057894109064988161

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

4.191 × 10⁹⁸(99-digit number)

41915911356973627764…74115788218129976319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.191 × 10⁹⁸(99-digit number)

41915911356973627764…74115788218129976321

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