Block #322,346

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/20/2013, 10:37:58 PM · Difficulty 10.1946 · 6,514,402 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

170d3f11190d457ae6312ecf899d8a8be89f06ce66a48b0d60f568fbbc2e8834

View on Chainz ↗

Height

#322,346

Difficulty

10.194568

Transactions

Size

2.37 KB

Version

Bits

0a31cf3b

Nonce

128,432

Timestamp

12/20/2013, 10:37:58 PM

Confirmations

6,514,402

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

f3a67d8b2e127f479dde62ba8c6421deddb350a7658c1e9f1831da9fd816a730

Transactions (4)

Coinbase56943260949663…1592c5d40020ea

1 in → 1 out9.6500 XPM110 B

AeKNrjNj…1NEq95Ta

3a7a3fb8b400d3…3ef71b4fe4a056

2 in → 7 out19.4300 XPM477 B

AYtJVduZ…HTRow78m AT5RKYn3…6ZWnx9o7 AeKNrjNj…1NEq95Ta AMbPepnb…sLphYiF8 AU1g12VV…CxSBsrgG

5ce5623b4413c7…599ff882f702c4

8 in → 2 out65.5350 XPM1.23 KB

AMCokwYa…aEBv5DEJ AefEiV2E…5xsLV8Le

b075cf9e1638c9…208553fa2517b7

3 in → 1 out3.0180 XPM488 B

AGKRp55o…EDcAuTdP

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.

5.297 × 10⁹⁷(98-digit number)

52973182191225396082…62191696979489198079

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

5.297 × 10⁹⁷(98-digit number)

52973182191225396082…62191696979489198079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.297 × 10⁹⁷(98-digit number)

52973182191225396082…62191696979489198081

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

1.059 × 10⁹⁸(99-digit number)

10594636438245079216…24383393958978396159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.059 × 10⁹⁸(99-digit number)

10594636438245079216…24383393958978396161

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

2.118 × 10⁹⁸(99-digit number)

21189272876490158433…48766787917956792319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.118 × 10⁹⁸(99-digit number)

21189272876490158433…48766787917956792321

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

4.237 × 10⁹⁸(99-digit number)

42378545752980316866…97533575835913584639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.237 × 10⁹⁸(99-digit number)

42378545752980316866…97533575835913584641

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

8.475 × 10⁹⁸(99-digit number)

84757091505960633732…95067151671827169279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.475 × 10⁹⁸(99-digit number)

84757091505960633732…95067151671827169281

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 #322,346

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