Block #212,554

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/16/2013, 9:04:28 AM · Difficulty 9.9190 · 6,603,773 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9242f0c64e4d4223e13647c64a24228eb5fb9b2912fb2562a466072de540d3f2

View on Chainz ↗

Height

#212,554

Difficulty

9.918967

Transactions

Size

2.99 KB

Version

Bits

09eb4166

Nonce

258,044

Timestamp

10/16/2013, 9:04:28 AM

Confirmations

6,603,773

Mined by

⛏️ P2SHAdaUfNWzq3psoSPVfa6fSAEcYr3GgD9yxT

Merkle Root

4683ccdda767af5227f1ab0eec24ac87ff6e4b841c273d7c7fe0dc884475c579

Transactions (4)

Coinbase1d7216b89bf439…7008b4acd52aab

1 in → 1 out10.2000 XPM109 B

AdaUfNWz…3GgD9yxT

4589ca878b20aa…f25a1f2ff68a0a

1 in → 2 out10.1600 XPM192 B

AFz9fXym…wh4UqpkL AXQMEcoH…9vdAxtdW

0e5295d8018183…d3567eacc527e9

1 in → 2 out10.1600 XPM227 B

ASuoUi24…FwBoFbxd ASiyinud…8LUKoSE5

7f6b89fcd72403…3b0fa2e473ce23

16 in → 2 out12.0100 XPM2.39 KB

AR8gm83i…GC9D5nDT APSnWrVT…cFXwApAE

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.

6.767 × 10⁹²(93-digit number)

67674652715069253783…42139318118523376639

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

6.767 × 10⁹²(93-digit number)

67674652715069253783…42139318118523376639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.767 × 10⁹²(93-digit number)

67674652715069253783…42139318118523376641

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

1.353 × 10⁹³(94-digit number)

13534930543013850756…84278636237046753279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.353 × 10⁹³(94-digit number)

13534930543013850756…84278636237046753281

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

2.706 × 10⁹³(94-digit number)

27069861086027701513…68557272474093506559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.706 × 10⁹³(94-digit number)

27069861086027701513…68557272474093506561

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

5.413 × 10⁹³(94-digit number)

54139722172055403026…37114544948187013119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.413 × 10⁹³(94-digit number)

54139722172055403026…37114544948187013121

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

1.082 × 10⁹⁴(95-digit number)

10827944434411080605…74229089896374026239

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 #212,554

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