Block #243,389

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 6:47:41 AM · Difficulty 9.9614 · 6,587,287 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2fa838e72165eb362524ceb7ea5e3e157cec54655c5b5f33600ecfd0480d8dd6

View on Chainz ↗

Height

#243,389

Difficulty

9.961370

Transactions

Size

1.68 KB

Version

Bits

09f61c59

Nonce

1,791

Timestamp

11/4/2013, 6:47:41 AM

Confirmations

6,587,287

Mined by

⛏️ RwBOAHkgKuuD216cYGGsRhDqkEkY9oTkWqWiw1

Merkle Root

f902d7fb2bdf367fec98b0f5d1131094f16c0bb3f0530b0b28ea7d889d5d39bf

Transactions (1)

Coinbasef902d7fb2bdf36…ea7d889d5d39bf

1 in → 46 out10.0400 XPM1.59 KB

AHkgKuuD…TkWqWiw1 ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY AG6v13Uf…pSStLmVN

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.

2.506 × 10⁹⁷(98-digit number)

25065886065963185307…58263024919222039479

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

2.506 × 10⁹⁷(98-digit number)

25065886065963185307…58263024919222039479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.506 × 10⁹⁷(98-digit number)

25065886065963185307…58263024919222039481

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

5.013 × 10⁹⁷(98-digit number)

50131772131926370614…16526049838444078959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.013 × 10⁹⁷(98-digit number)

50131772131926370614…16526049838444078961

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

1.002 × 10⁹⁸(99-digit number)

10026354426385274122…33052099676888157919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.002 × 10⁹⁸(99-digit number)

10026354426385274122…33052099676888157921

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

2.005 × 10⁹⁸(99-digit number)

20052708852770548245…66104199353776315839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.005 × 10⁹⁸(99-digit number)

20052708852770548245…66104199353776315841

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

4.010 × 10⁹⁸(99-digit number)

40105417705541096491…32208398707552631679

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 #243,389

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