Block #308,710

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/13/2013, 5:55:20 AM · Difficulty 9.9946 · 6,494,668 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

364599fd5aa44c5c8e1c8c0d0c238103044e7acbb5e681a69187ece300f39932

View on Chainz ↗

Height

#308,710

Difficulty

9.994595

Transactions

Size

1.15 KB

Version

Bits

09fe9dc2

Nonce

82,825

Timestamp

12/13/2013, 5:55:20 AM

Confirmations

6,494,668

Mined by

⛏️ aR5AZH5kg1mWFqMQk484uLBE8F8TTYt7tEZrf

Merkle Root

ad0f5e86aa410d273e4fb2b5030b582c10e3df462fd1fa9a75193b7e5bfd8d70

Transactions (1)

Coinbasead0f5e86aa410d…193b7e5bfd8d70

1 in → 30 out9.9800 XPM1.06 KB

AZH5kg1m…Yt7tEZrf Aez256Un…NhdMBMc4 AMR89gp5…oZEXFX4Z AXLVWw1P…9Fa7UDfG AMRko8yH…hzixtWbJ

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.

7.620 × 10⁹³(94-digit number)

76203131040236777435…21618341642833584399

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

7.620 × 10⁹³(94-digit number)

76203131040236777435…21618341642833584399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.620 × 10⁹³(94-digit number)

76203131040236777435…21618341642833584401

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

1.524 × 10⁹⁴(95-digit number)

15240626208047355487…43236683285667168799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.524 × 10⁹⁴(95-digit number)

15240626208047355487…43236683285667168801

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

3.048 × 10⁹⁴(95-digit number)

30481252416094710974…86473366571334337599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.048 × 10⁹⁴(95-digit number)

30481252416094710974…86473366571334337601

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

6.096 × 10⁹⁴(95-digit number)

60962504832189421948…72946733142668675199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.096 × 10⁹⁴(95-digit number)

60962504832189421948…72946733142668675201

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

1.219 × 10⁹⁵(96-digit number)

12192500966437884389…45893466285337350399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.219 × 10⁹⁵(96-digit number)

12192500966437884389…45893466285337350401

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