Block #233,411

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/29/2013, 5:12:53 PM · Difficulty 9.9425 · 6,581,067 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

29ed0933c59ea740a0c29a5d16355b9cb98cec4a4ec73dac77a8243fa3af4e8e

View on Chainz ↗

Height

#233,411

Difficulty

9.942464

Transactions

Size

734 B

Version

Bits

09f1454d

Nonce

12,598

Timestamp

10/29/2013, 5:12:53 PM

Confirmations

6,581,067

Mined by

⛏️ P2SHAegQsT98wGG7b4xTzF2AKiHMDWs4v5epgp

Merkle Root

105294190f33cf587f1d0afd3d916818c9fbd6026695c45565d89ba60731a4f2

Transactions (2)

Coinbasef2bade0a8da87e…92806c9eed923e

1 in → 1 out10.1100 XPM109 B

AegQsT98…s4v5epgp

672ff14f95447a…6da066eae5871b

4 in → 2 out40.5200 XPM535 B

AUWSHaqw…p7HvJXAD AV6ArHNw…VEUNbSGe

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.

1.111 × 10⁹⁵(96-digit number)

11115069073822317714…04105847165528563199

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

1.111 × 10⁹⁵(96-digit number)

11115069073822317714…04105847165528563199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.111 × 10⁹⁵(96-digit number)

11115069073822317714…04105847165528563201

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

2.223 × 10⁹⁵(96-digit number)

22230138147644635429…08211694331057126399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.223 × 10⁹⁵(96-digit number)

22230138147644635429…08211694331057126401

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

4.446 × 10⁹⁵(96-digit number)

44460276295289270858…16423388662114252799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.446 × 10⁹⁵(96-digit number)

44460276295289270858…16423388662114252801

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

8.892 × 10⁹⁵(96-digit number)

88920552590578541716…32846777324228505599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.892 × 10⁹⁵(96-digit number)

88920552590578541716…32846777324228505601

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

1.778 × 10⁹⁶(97-digit number)

17784110518115708343…65693554648457011199

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 #233,411

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