Block #237,743

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/1/2013, 5:17:04 AM · Difficulty 9.9504 · 6,561,566 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

535528cb78220c5ed92bd9b24d6f0cc9d3841b0ef8c1e51b60927a50b4f71f79

View on Chainz ↗

Height

#237,743

Difficulty

9.950389

Transactions

Size

1.81 KB

Version

Bits

09f34cb7

Nonce

6,631

Timestamp

11/1/2013, 5:17:04 AM

Confirmations

6,561,566

Mined by

⛏️ Rs8ARy21RErJbHr8Mrr5vpYP14eN46pBWtQJ2

Merkle Root

608cb2db1773ef53fc76048fa5db2d995854b961af8dc5b3a39da93f0c2fb4d2

Transactions (1)

Coinbase608cb2db1773ef…9da93f0c2fb4d2

1 in → 50 out10.0600 XPM1.72 KB

ARy21REr…6pBWtQJ2 ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC ARQrJViM…5cGXU5z4 AcEnwywz…vZtt2xTs

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.

1.851 × 10⁹³(94-digit number)

18519780749088722157…31250442803192473599

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

1.851 × 10⁹³(94-digit number)

18519780749088722157…31250442803192473599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.851 × 10⁹³(94-digit number)

18519780749088722157…31250442803192473601

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

3.703 × 10⁹³(94-digit number)

37039561498177444314…62500885606384947199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.703 × 10⁹³(94-digit number)

37039561498177444314…62500885606384947201

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

7.407 × 10⁹³(94-digit number)

74079122996354888628…25001771212769894399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.407 × 10⁹³(94-digit number)

74079122996354888628…25001771212769894401

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

1.481 × 10⁹⁴(95-digit number)

14815824599270977725…50003542425539788799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.481 × 10⁹⁴(95-digit number)

14815824599270977725…50003542425539788801

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

2.963 × 10⁹⁴(95-digit number)

29631649198541955451…00007084851079577599

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