Block #307,936

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 8:34:35 PM · Difficulty 9.9943 · 6,501,997 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1541c9319903e31445e65678bfd3ee3a2879360127075ea968b6b75f48008832

View on Chainz ↗

Height

#307,936

Difficulty

9.994338

Transactions

Size

1.01 KB

Version

Bits

09fe8cee

Nonce

148,245

Timestamp

12/12/2013, 8:34:35 PM

Confirmations

6,501,997

Mined by

⛏️ aRAYtDvcGsMH2GY5bD4Hc2rArhMdVuAcA7m7

Merkle Root

3cc8bcc811ba840d6e066bd59c837edae3eecb34bcd7b44d52ac03d111d70ef1

Transactions (1)

Coinbase3cc8bcc811ba84…ac03d111d70ef1

1 in → 26 out10.0000 XPM947 B

AYtDvcGs…VuAcA7m7 Aac9Hjdg…P4ktypc3 AcC2zSod…rtWatH79 AYcLTeXR…bscgPops AG5YAjec…VhA4Aeh1

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.

7.943 × 10⁹⁸(99-digit number)

79432715305863842354…54001642355903211519

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

7.943 × 10⁹⁸(99-digit number)

79432715305863842354…54001642355903211519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.943 × 10⁹⁸(99-digit number)

79432715305863842354…54001642355903211521

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

1.588 × 10⁹⁹(100-digit number)

15886543061172768470…08003284711806423039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.588 × 10⁹⁹(100-digit number)

15886543061172768470…08003284711806423041

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

3.177 × 10⁹⁹(100-digit number)

31773086122345536941…16006569423612846079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.177 × 10⁹⁹(100-digit number)

31773086122345536941…16006569423612846081

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

6.354 × 10⁹⁹(100-digit number)

63546172244691073883…32013138847225692159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.354 × 10⁹⁹(100-digit number)

63546172244691073883…32013138847225692161

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

1.270 × 10¹⁰⁰(101-digit number)

12709234448938214776…64026277694451384319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.270 × 10¹⁰⁰(101-digit number)

12709234448938214776…64026277694451384321

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 #307,936

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