Block #303,753

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/10/2013, 1:26:26 PM · Difficulty 9.9931 · 6,504,229 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9357694fae6d1e0b76160c765f5b750944ef2e6dfedffcaad0e389c0d9db0383

View on Chainz ↗

Height

#303,753

Difficulty

9.993113

Transactions

Size

1.09 KB

Version

Bits

09fe3ca7

Nonce

53,758

Timestamp

12/10/2013, 1:26:26 PM

Confirmations

6,504,229

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

3a6af86a31126081663b8ed1f9099578b94c58bad2fc9a461ceefc0c7d0eee20

Transactions (3)

Coinbase32d1c746d08398…082cd4687a6b97

1 in → 1 out10.0200 XPM110 B

AeKNrjNj…1NEq95Ta

b5da2fcbaf4836…09dd04a470177e

3 in → 10 out30.1306 XPM692 B

AQDhQSFN…reK5U7Zs AeKNrjNj…1NEq95Ta AaGFGuxk…yHqbvR6P AbZdyDXS…aEcuKheX AKbpoask…dtBVWNrZ

3daed6dc33a4a2…3afb1834d93577

1 in → 2 out1.6602 XPM225 B

ASncXusG…FttReQ5u AWaQGtMF…hkZT6dTB

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.

3.215 × 10⁹¹(92-digit number)

32156919894315444845…88059282892068704319

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

3.215 × 10⁹¹(92-digit number)

32156919894315444845…88059282892068704319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.215 × 10⁹¹(92-digit number)

32156919894315444845…88059282892068704321

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

6.431 × 10⁹¹(92-digit number)

64313839788630889691…76118565784137408639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.431 × 10⁹¹(92-digit number)

64313839788630889691…76118565784137408641

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

1.286 × 10⁹²(93-digit number)

12862767957726177938…52237131568274817279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.286 × 10⁹²(93-digit number)

12862767957726177938…52237131568274817281

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

2.572 × 10⁹²(93-digit number)

25725535915452355876…04474263136549634559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.572 × 10⁹²(93-digit number)

25725535915452355876…04474263136549634561

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

5.145 × 10⁹²(93-digit number)

51451071830904711752…08948526273099269119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.145 × 10⁹²(93-digit number)

51451071830904711752…08948526273099269121

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 #303,753

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