Block #214,936

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/17/2013, 6:54:45 PM · Difficulty 9.9245 · 6,594,167 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

12bf5a33b60a129300eba5bdb762bdb649f84ef3e7725908b4f5d441fa2456d8

View on Chainz ↗

Height

#214,936

Difficulty

9.924514

Transactions

Size

5.63 KB

Version

Bits

09ecacf3

Nonce

1,164,867,015

Timestamp

10/17/2013, 6:54:45 PM

Confirmations

6,594,167

Mined by

⛏️ GR`2AaEoqAqJmWuC9ZbGjvDTTk7PuydmRpi31P

Merkle Root

6923a7287fea78ef88ae6402fc6203895aad6916ed7893f1d9ba178974761521

Transactions (1)

Coinbase6923a7287fea78…ba178974761521

1 in → 165 out10.0800 XPM5.54 KB

AaEoqAqJ…dmRpi31P AM4zvBDn…dBXWgwDw AQHscFmz…f7iBBj6f AGbRhLj1…nZcEQFqQ AVeHc9d8…MRstqd4p

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.

5.654 × 10⁹¹(92-digit number)

56543091995240700272…13435044470508682579

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

5.654 × 10⁹¹(92-digit number)

56543091995240700272…13435044470508682579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.654 × 10⁹¹(92-digit number)

56543091995240700272…13435044470508682581

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

1.130 × 10⁹²(93-digit number)

11308618399048140054…26870088941017365159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.130 × 10⁹²(93-digit number)

11308618399048140054…26870088941017365161

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

2.261 × 10⁹²(93-digit number)

22617236798096280109…53740177882034730319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.261 × 10⁹²(93-digit number)

22617236798096280109…53740177882034730321

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

4.523 × 10⁹²(93-digit number)

45234473596192560218…07480355764069460639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.523 × 10⁹²(93-digit number)

45234473596192560218…07480355764069460641

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

9.046 × 10⁹²(93-digit number)

90468947192385120436…14960711528138921279

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 #214,936

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