Block #236,783

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 4:32:51 PM · Difficulty 9.9484 · 6,580,384 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

96ee742960048a3c9c5bf9bb28f6a16c3110b692e6e0eb563171ae2ca01b891d

View on Chainz ↗

Height

#236,783

Difficulty

9.948370

Transactions

Size

1.53 KB

Version

Bits

09f2c862

Nonce

11,914

Timestamp

10/31/2013, 4:32:51 PM

Confirmations

6,580,384

Mined by

⛏️ P2SHAeL7UAFbYJxtsFPY1Wp7S8F2EUW9mPDyGL

Merkle Root

428f0318d27598e10d7cdfdc743d50d3dc4c799ff3bd3f18d30db411b6390bc4

Transactions (3)

Coinbase2a6a162daf2afb…b886a65a8c3fb6

1 in → 2 out10.1100 XPM136 B

AeL7UAFb…W9mPDyGL ALfEGCwh…VawujfMm

837cdabadf3eec…0a4721c8a68a7c

6 in → 2 out12.0303 XPM965 B

APFRKs74…2TdBTb3P Ad94G1nm…PkHWgZEN

411dfb02c15c3d…1aa2f5cd712b51

2 in → 2 out5.9188 XPM373 B

Af4yQ1mT…ukMmaiAe AN3QK9wE…SHQv3wVg

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.

1.504 × 10⁹⁹(100-digit number)

15045282884899338949…39555253576948684799

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

1.504 × 10⁹⁹(100-digit number)

15045282884899338949…39555253576948684799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.504 × 10⁹⁹(100-digit number)

15045282884899338949…39555253576948684801

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

3.009 × 10⁹⁹(100-digit number)

30090565769798677899…79110507153897369599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.009 × 10⁹⁹(100-digit number)

30090565769798677899…79110507153897369601

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

6.018 × 10⁹⁹(100-digit number)

60181131539597355799…58221014307794739199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.018 × 10⁹⁹(100-digit number)

60181131539597355799…58221014307794739201

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

1.203 × 10¹⁰⁰(101-digit number)

12036226307919471159…16442028615589478399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.203 × 10¹⁰⁰(101-digit number)

12036226307919471159…16442028615589478401

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

2.407 × 10¹⁰⁰(101-digit number)

24072452615838942319…32884057231178956799

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 #236,783

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