Block #1,350,082

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2015, 6:11:15 PM · Difficulty 10.8050 · 5,460,868 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d3c2a6d4b7dc425a4a4120b6962ba516dbddc0eda2eed283f980f604b174432a

View on Chainz ↗

Height

#1,350,082

Difficulty

10.804986

Transactions

Size

2.24 KB

Version

Bits

0ace1396

Nonce

389,664,134

Timestamp

12/1/2015, 6:11:15 PM

Confirmations

5,460,868

Mined by

⛏️ P2SHAbtrN6jygEjc4fVz5RepTz5cF7eAXdAfYN

Merkle Root

3fbdd158317b95fb512a2cb9ca59ef594bc503540b29cfef2abcc173318a0499

Transactions (3)

Coinbase672a52fb29de67…4ae22eaa5038b2

1 in → 1 out8.6500 XPM110 B

AbtrN6jy…eAXdAfYN

264f196834ef18…48081d09a07ef5

7 in → 2 out23.2548 XPM1.09 KB

AWtM9hQs…qXzQB7Yb AbecWDS9…1vtToSML

ca3fb16251af21…2dce2e0b2c2348

1 in → 24 out124.8942 XPM975 B

AXisyknQ…ZTUGCTrx APAuH928…YD2GXeNG AQGtiJuV…jTtoappo AKsSBvGX…wzCKCnbZ APRw2zCo…E65r9U3o

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.

1.068 × 10⁹⁶(97-digit number)

10686010434541460452…98166648972982845439

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

1.068 × 10⁹⁶(97-digit number)

10686010434541460452…98166648972982845439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.068 × 10⁹⁶(97-digit number)

10686010434541460452…98166648972982845441

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

2.137 × 10⁹⁶(97-digit number)

21372020869082920904…96333297945965690879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.137 × 10⁹⁶(97-digit number)

21372020869082920904…96333297945965690881

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

4.274 × 10⁹⁶(97-digit number)

42744041738165841809…92666595891931381759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.274 × 10⁹⁶(97-digit number)

42744041738165841809…92666595891931381761

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

8.548 × 10⁹⁶(97-digit number)

85488083476331683618…85333191783862763519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.548 × 10⁹⁶(97-digit number)

85488083476331683618…85333191783862763521

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

1.709 × 10⁹⁷(98-digit number)

17097616695266336723…70666383567725527039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.709 × 10⁹⁷(98-digit number)

17097616695266336723…70666383567725527041

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 #1,350,082

Cookie Preferences