Block #1,120,791

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/21/2015, 9:40:19 AM · Difficulty 10.9362 · 5,674,809 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cc98b42a3bb0f4e1813a6bff1afb999affc4b521b3fa37ec40b189e8eef49f2b

View on Chainz ↗

Height

#1,120,791

Difficulty

10.936157

Transactions

Size

94.11 KB

Version

Bits

0aefa802

Nonce

634,218,164

Timestamp

6/21/2015, 9:40:19 AM

Confirmations

5,674,809

Mined by

⛏️ P2SHAby5KiwHiGF8w18nah3ScPNYV2LZLo6kKR

Merkle Root

8c6b61df83867eb8cae2a4aa5536d28e203f62787406ed6a4aa5422addd92260

Transactions (2)

Coinbased00704fe65c879…a2df6258968f8b

1 in → 1 out9.3300 XPM110 B

Aby5KiwH…LZLo6kKR

1757606b74b8b9…ec6c19fda62312

649 in → 2 out1500.0100 XPM93.91 KB

AYKArr5V…V9VqiqCZ ALgBMqKu…sXhd8qEo

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.

1.724 × 10⁹⁶(97-digit number)

17246887317701956195…55387399394386143999

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

1.724 × 10⁹⁶(97-digit number)

17246887317701956195…55387399394386143999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.724 × 10⁹⁶(97-digit number)

17246887317701956195…55387399394386144001

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

3.449 × 10⁹⁶(97-digit number)

34493774635403912390…10774798788772287999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.449 × 10⁹⁶(97-digit number)

34493774635403912390…10774798788772288001

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

6.898 × 10⁹⁶(97-digit number)

68987549270807824780…21549597577544575999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.898 × 10⁹⁶(97-digit number)

68987549270807824780…21549597577544576001

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

1.379 × 10⁹⁷(98-digit number)

13797509854161564956…43099195155089151999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.379 × 10⁹⁷(98-digit number)

13797509854161564956…43099195155089152001

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

2.759 × 10⁹⁷(98-digit number)

27595019708323129912…86198390310178303999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.759 × 10⁹⁷(98-digit number)

27595019708323129912…86198390310178304001

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