Block #1,320,094

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/9/2015, 6:03:28 PM · Difficulty 10.8599 · 5,492,240 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8eefc78022ae05aaed1d536b55e883115e3c961e36b7873fd74032844272117f

View on Chainz ↗

Height

#1,320,094

Difficulty

10.859885

Transactions

Size

3.02 KB

Version

Bits

0adc2165

Nonce

1,153,644,078

Timestamp

11/9/2015, 6:03:28 PM

Confirmations

5,492,240

Mined by

⛏️ P2SHAHhywqFwTa4YWZ2itcWCFuoR2TuRUyANs7

Merkle Root

eb0153c1df31bacf662bdacf92175b2ea53793f2c7f1ea4e4b92cd1cf22b89f0

Transactions (2)

Coinbasedd4dc2b3d8dd54…540557df2f0796

1 in → 1 out8.5100 XPM110 B

AHhywqFw…uRUyANs7

51b8fe50e7dcb1…28ecb10f6c465d

19 in → 2 out49.7500 XPM2.82 KB

AZc8sasn…9ZYCFMf1 AJPzCU2m…bhUDEQ9z

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.

1.053 × 10⁹⁶(97-digit number)

10530563236276919276…27623303891858639359

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

1.053 × 10⁹⁶(97-digit number)

10530563236276919276…27623303891858639359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.053 × 10⁹⁶(97-digit number)

10530563236276919276…27623303891858639361

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

2.106 × 10⁹⁶(97-digit number)

21061126472553838552…55246607783717278719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.106 × 10⁹⁶(97-digit number)

21061126472553838552…55246607783717278721

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

4.212 × 10⁹⁶(97-digit number)

42122252945107677105…10493215567434557439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.212 × 10⁹⁶(97-digit number)

42122252945107677105…10493215567434557441

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

8.424 × 10⁹⁶(97-digit number)

84244505890215354211…20986431134869114879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.424 × 10⁹⁶(97-digit number)

84244505890215354211…20986431134869114881

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

1.684 × 10⁹⁷(98-digit number)

16848901178043070842…41972862269738229759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.684 × 10⁹⁷(98-digit number)

16848901178043070842…41972862269738229761

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 #1,320,094

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