Block #292,659

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 8:53:07 PM · Difficulty 9.9904 · 6,510,904 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

93cdf8cef1555bfc57fdd618a4ecbffb1fa512cc7c93a433a2fd7013e821737e

View on Chainz ↗

Height

#292,659

Difficulty

9.990375

Transactions

Size

1.05 KB

Version

Bits

09fd8934

Nonce

127,261

Timestamp

12/3/2013, 8:53:07 PM

Confirmations

6,510,904

Mined by

⛏️ 3waRDARzXge7STrHg8ZTMRW57MCNAWRCEjL5oYm

Merkle Root

9f4d2d1aa9e7d29deff318aea37ff78d05e676f8bc68142f9d68d40ddbb9fd01

Transactions (1)

Coinbase9f4d2d1aa9e7d2…68d40ddbb9fd01

1 in → 27 out10.0000 XPM980 B

ARzXge7S…CEjL5oYm AZninDSu…FvgDMwC4 AQwRN8bE…V8PsTcY9 AMdvB6BS…DPq9FYdA ARskhKeb…UgDvvX9P

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.

1.098 × 10⁹⁶(97-digit number)

10988775721445709023…22222420700254423999

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

1.098 × 10⁹⁶(97-digit number)

10988775721445709023…22222420700254423999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.098 × 10⁹⁶(97-digit number)

10988775721445709023…22222420700254424001

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

2.197 × 10⁹⁶(97-digit number)

21977551442891418046…44444841400508847999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.197 × 10⁹⁶(97-digit number)

21977551442891418046…44444841400508848001

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

4.395 × 10⁹⁶(97-digit number)

43955102885782836092…88889682801017695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.395 × 10⁹⁶(97-digit number)

43955102885782836092…88889682801017696001

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

8.791 × 10⁹⁶(97-digit number)

87910205771565672184…77779365602035391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.791 × 10⁹⁶(97-digit number)

87910205771565672184…77779365602035392001

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

1.758 × 10⁹⁷(98-digit number)

17582041154313134436…55558731204070783999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.758 × 10⁹⁷(98-digit number)

17582041154313134436…55558731204070784001

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