Block #1,324,940

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/13/2015, 6:58:38 AM · Difficulty 10.8530 · 5,480,237 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

367d2b04c83b3f78a654943c870f88eb4a2dc1edd432a0745394d8cf30bd6eeb

View on Chainz ↗

Height

#1,324,940

Difficulty

10.853007

Transactions

Size

16.33 KB

Version

Bits

0ada5eae

Nonce

1,013,610,220

Timestamp

11/13/2015, 6:58:38 AM

Confirmations

5,480,237

Mined by

⛏️ P2SHAJjc4AwxUod2GCjxgXJYcTJCEbxoK8kSLs

Merkle Root

97e4c28811592c9029f23b62a74b63111e3fd07840ef298a325282437ce94e39

Transactions (2)

Coinbaseed4faefc8af996…179a8b3804be39

1 in → 1 out8.6500 XPM110 B

AJjc4Awx…xoK8kSLs

3a42be9081bfd1…e59010e833ba59

111 in → 2 out500.0100 XPM16.13 KB

AH4mJ4oJ…dtcVyAKQ AJjnK9uC…VreFquR4

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.

2.986 × 10⁹⁵(96-digit number)

29864045149983847922…22473749646425291599

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

2.986 × 10⁹⁵(96-digit number)

29864045149983847922…22473749646425291599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.986 × 10⁹⁵(96-digit number)

29864045149983847922…22473749646425291601

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

5.972 × 10⁹⁵(96-digit number)

59728090299967695844…44947499292850583199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.972 × 10⁹⁵(96-digit number)

59728090299967695844…44947499292850583201

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

1.194 × 10⁹⁶(97-digit number)

11945618059993539168…89894998585701166399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.194 × 10⁹⁶(97-digit number)

11945618059993539168…89894998585701166401

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

2.389 × 10⁹⁶(97-digit number)

23891236119987078337…79789997171402332799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.389 × 10⁹⁶(97-digit number)

23891236119987078337…79789997171402332801

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

4.778 × 10⁹⁶(97-digit number)

47782472239974156675…59579994342804665599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.778 × 10⁹⁶(97-digit number)

47782472239974156675…59579994342804665601

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