Block #233,975

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/30/2013, 1:26:16 AM · Difficulty 9.9433 · 6,583,797 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

daa45ec542142e424a17715149c2d2b150a2c1b93b15d84323fb46a92227ecfc

View on Chainz ↗

Height

#233,975

Difficulty

9.943308

Transactions

Size

2.11 KB

Version

Bits

09f17ca4

Nonce

39,815

Timestamp

10/30/2013, 1:26:16 AM

Confirmations

6,583,797

Mined by

⛏️ Rp_EAMypZdXSN9SRf28auDeE3guPFj5jJKu8wP

Merkle Root

186b409ef6fecddc40c75e6bfdbb46bc2411ca7388f64b4af2795116d707bb14

Transactions (1)

Coinbase186b409ef6fecd…795116d707bb14

1 in → 59 out10.0700 XPM2.02 KB

AMypZdXS…5jJKu8wP AFqKfjez…qX9Ace3g AdwTEXyC…NwbVbqZV Aaox8Rxx…XTyyJXVx AQtzUSwq…htAuF3yC

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.

1.966 × 10⁹²(93-digit number)

19667100741193499472…04805565721620063359

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

1.966 × 10⁹²(93-digit number)

19667100741193499472…04805565721620063359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.966 × 10⁹²(93-digit number)

19667100741193499472…04805565721620063361

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

3.933 × 10⁹²(93-digit number)

39334201482386998945…09611131443240126719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.933 × 10⁹²(93-digit number)

39334201482386998945…09611131443240126721

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

7.866 × 10⁹²(93-digit number)

78668402964773997891…19222262886480253439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.866 × 10⁹²(93-digit number)

78668402964773997891…19222262886480253441

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

1.573 × 10⁹³(94-digit number)

15733680592954799578…38444525772960506879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.573 × 10⁹³(94-digit number)

15733680592954799578…38444525772960506881

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

3.146 × 10⁹³(94-digit number)

31467361185909599156…76889051545921013759

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 #233,975

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