Block #211,344

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/15/2013, 4:14:21 PM · Difficulty 9.9156 · 6,591,188 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1836c3c7c5dd664f3c9a188775f0517d7497f4f2c34b5b78f28aa44f4c72c397

View on Chainz ↗

Height

#211,344

Difficulty

9.915575

Transactions

Size

5.76 KB

Version

Bits

09ea6323

Nonce

1,164,809,850

Timestamp

10/15/2013, 4:14:21 PM

Confirmations

6,591,188

Mined by

⛏️ 9RAWhVP6YLa69yHWVdEaKnVbTY8CFFDSHQcj

Merkle Root

5f7b3638ecb0dd9e4fdf18422d032b0200474258b0bf6a8f16f49ed7f52c4a6f

Transactions (1)

Coinbase5f7b3638ecb0dd…f49ed7f52c4a6f

1 in → 169 out10.1000 XPM5.67 KB

AWhVP6YL…FFDSHQcj AY2xJ15f…mp4Huewu AUTB45aM…s8yjKL4h AKeDh1uS…Th9Hwfjg AZ4gvP32…ukKsCiYr

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.

3.691 × 10⁹⁴(95-digit number)

36919118596620674343…00744632724825511679

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

3.691 × 10⁹⁴(95-digit number)

36919118596620674343…00744632724825511679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.691 × 10⁹⁴(95-digit number)

36919118596620674343…00744632724825511681

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

7.383 × 10⁹⁴(95-digit number)

73838237193241348687…01489265449651023359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.383 × 10⁹⁴(95-digit number)

73838237193241348687…01489265449651023361

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

1.476 × 10⁹⁵(96-digit number)

14767647438648269737…02978530899302046719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.476 × 10⁹⁵(96-digit number)

14767647438648269737…02978530899302046721

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

2.953 × 10⁹⁵(96-digit number)

29535294877296539475…05957061798604093439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.953 × 10⁹⁵(96-digit number)

29535294877296539475…05957061798604093441

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

5.907 × 10⁹⁵(96-digit number)

59070589754593078950…11914123597208186879

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