Block #304,048

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/10/2013, 5:27:05 PM · Difficulty 9.9932 · 6,506,849 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a05be06870ba6628dd45cd2e542557cc62e4f4ad5257150d2e487b69086b4b27

View on Chainz ↗

Height

#304,048

Difficulty

9.993196

Transactions

Size

1.11 KB

Version

Bits

09fe421b

Nonce

12,917

Timestamp

12/10/2013, 5:27:05 PM

Confirmations

6,506,849

Mined by

⛏️ aRNAQBqYP46p1nBDCM2eHR9LC8H9FNcWpkngb

Merkle Root

ce06ff9417f0b5701fade5831dea8d434fefc5fa66e793a93e31add3aed4f055

Transactions (1)

Coinbasece06ff9417f0b5…31add3aed4f055

1 in → 29 out9.9800 XPM1.02 KB

AQBqYP46…NcWpkngb AaJwNkvB…uqCwyjYa AQf7sjuh…sNY5fXpu AHyMdFt5…QAHen7Mb AYtDvcGs…VuAcA7m7

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.

1.391 × 10⁹²(93-digit number)

13914025204665320456…89293360699825272719

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

1.391 × 10⁹²(93-digit number)

13914025204665320456…89293360699825272719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.391 × 10⁹²(93-digit number)

13914025204665320456…89293360699825272721

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

2.782 × 10⁹²(93-digit number)

27828050409330640912…78586721399650545439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.782 × 10⁹²(93-digit number)

27828050409330640912…78586721399650545441

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

5.565 × 10⁹²(93-digit number)

55656100818661281824…57173442799301090879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.565 × 10⁹²(93-digit number)

55656100818661281824…57173442799301090881

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

1.113 × 10⁹³(94-digit number)

11131220163732256364…14346885598602181759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.113 × 10⁹³(94-digit number)

11131220163732256364…14346885598602181761

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

2.226 × 10⁹³(94-digit number)

22262440327464512729…28693771197204363519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.226 × 10⁹³(94-digit number)

22262440327464512729…28693771197204363521

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 #304,048

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