Block #296,273

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/5/2013, 10:25:29 PM · Difficulty 9.9916 · 6,511,756 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

532804b972349a3a46ff63df5fddbac39fbfb9f054457bcd0360b339e17bc2ef

View on Chainz ↗

Height

#296,273

Difficulty

9.991644

Transactions

Size

1.08 KB

Version

Bits

09fddc65

Nonce

259,297

Timestamp

12/5/2013, 10:25:29 PM

Confirmations

6,511,756

Mined by

⛏️ QaRARzXge7STrHg8ZTMRW57MCNAWRCEjL5oYm

Merkle Root

ed237f04e15e2e04ad9db045c870cb9820fbfed46b580791b07eb02f4a46224e

Transactions (1)

Coinbaseed237f04e15e2e…7eb02f4a46224e

1 in → 28 out9.9777 XPM1014 B

ARzXge7S…CEjL5oYm AWQyM49v…zN9UeNMm AQwRN8bE…V8PsTcY9 AYcLTeXR…bscgPops AWGfRMN3…Uoo3vXQw

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.

9.220 × 10⁸⁹(90-digit number)

92204128323574112927…25062428107227283419

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

9.220 × 10⁸⁹(90-digit number)

92204128323574112927…25062428107227283419

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.220 × 10⁸⁹(90-digit number)

92204128323574112927…25062428107227283421

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

1.844 × 10⁹⁰(91-digit number)

18440825664714822585…50124856214454566839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.844 × 10⁹⁰(91-digit number)

18440825664714822585…50124856214454566841

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

3.688 × 10⁹⁰(91-digit number)

36881651329429645171…00249712428909133679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.688 × 10⁹⁰(91-digit number)

36881651329429645171…00249712428909133681

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

7.376 × 10⁹⁰(91-digit number)

73763302658859290342…00499424857818267359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.376 × 10⁹⁰(91-digit number)

73763302658859290342…00499424857818267361

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

1.475 × 10⁹¹(92-digit number)

14752660531771858068…00998849715636534719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #296,273

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