Block #304,292

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/10/2013, 8:37:57 PM · Difficulty 9.9933 · 6,520,492 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7cad4418c1d62cf4ba6ad144784177fe9b3d2a56e9c84156918f48f1655c3b21

View on Chainz ↗

Height

#304,292

Difficulty

9.993275

Transactions

Size

1.08 KB

Version

Bits

09fe474a

Nonce

26,479

Timestamp

12/10/2013, 8:37:57 PM

Confirmations

6,520,492

Mined by

⛏️ aR{AMc6W7hqEjKWNAd1zz6cYugTghDv8ZFth2

Merkle Root

5367955a91a6f4d9accc792632384c7bd5ea161198f82b922e7c3572f0df1d7b

Transactions (1)

Coinbase5367955a91a6f4…7c3572f0df1d7b

1 in → 28 out9.9800 XPM1015 B

AMc6W7hq…Dv8ZFth2 AXpJhzaY…U6Qp8LwL AenXgLL6…ChwZjYpX AYtDvcGs…VuAcA7m7 AWu6Psms…uWWmCkLw

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.

2.865 × 10⁹³(94-digit number)

28652959338739412591…28814856347727730009

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

2.865 × 10⁹³(94-digit number)

28652959338739412591…28814856347727730009

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.865 × 10⁹³(94-digit number)

28652959338739412591…28814856347727730011

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

5.730 × 10⁹³(94-digit number)

57305918677478825182…57629712695455460019

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.730 × 10⁹³(94-digit number)

57305918677478825182…57629712695455460021

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

1.146 × 10⁹⁴(95-digit number)

11461183735495765036…15259425390910920039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.146 × 10⁹⁴(95-digit number)

11461183735495765036…15259425390910920041

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

2.292 × 10⁹⁴(95-digit number)

22922367470991530073…30518850781821840079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.292 × 10⁹⁴(95-digit number)

22922367470991530073…30518850781821840081

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

4.584 × 10⁹⁴(95-digit number)

45844734941983060146…61037701563643680159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.584 × 10⁹⁴(95-digit number)

45844734941983060146…61037701563643680161

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 #304,292

Cookie Preferences