Block #229,002

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/26/2013, 9:49:19 PM · Difficulty 9.9379 · 6,575,779 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

46462c92d479c8f10c213fb942573f542eeff0cab82ab4d72ec26d27873e910a

View on Chainz ↗

Height

#229,002

Difficulty

9.937907

Transactions

Size

1.41 KB

Version

Bits

09f01aa6

Nonce

16,777,453

Timestamp

10/26/2013, 9:49:19 PM

Confirmations

6,575,779

Mined by

⛏️ ~Rl8ARR7aRH6ng9G4v4WFreBpLwkEdne3DXGXZ

Merkle Root

a2e82138d64bce2632a0ea774fe084efa8a34bcf0ba8bc5c9362acdd41117e90

Transactions (1)

Coinbasea2e82138d64bce…62acdd41117e90

1 in → 38 out10.0900 XPM1.32 KB

ARR7aRH6…ne3DXGXZ AMbCuLHZ…WSoStwkc AU3PaCwF…92DCmeEV AWCfnjpk…hb1ovL8F Acs9SHrk…QJSB8SFG

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.

5.356 × 10⁹⁵(96-digit number)

53561267419751881283…57667106332993733879

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

5.356 × 10⁹⁵(96-digit number)

53561267419751881283…57667106332993733879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.356 × 10⁹⁵(96-digit number)

53561267419751881283…57667106332993733881

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

1.071 × 10⁹⁶(97-digit number)

10712253483950376256…15334212665987467759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.071 × 10⁹⁶(97-digit number)

10712253483950376256…15334212665987467761

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

2.142 × 10⁹⁶(97-digit number)

21424506967900752513…30668425331974935519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.142 × 10⁹⁶(97-digit number)

21424506967900752513…30668425331974935521

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

4.284 × 10⁹⁶(97-digit number)

42849013935801505026…61336850663949871039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.284 × 10⁹⁶(97-digit number)

42849013935801505026…61336850663949871041

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

8.569 × 10⁹⁶(97-digit number)

85698027871603010053…22673701327899742079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.569 × 10⁹⁶(97-digit number)

85698027871603010053…22673701327899742081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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