Block #234,328

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/30/2013, 6:30:23 AM · Difficulty 9.9439 · 6,561,816 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5fa38f1959e84f0513eb62724a2c402a4bbab00371cb32ea9df11f5207f8eec5

View on Chainz ↗

Height

#234,328

Difficulty

9.943867

Transactions

Size

1.78 KB

Version

Bits

09f1a141

Nonce

8,635

Timestamp

10/30/2013, 6:30:23 AM

Confirmations

6,561,816

Mined by

⛏️ XRp'4AKwqFUdzFNyMbekqhPUpd29CZJD4jGNKFN

Merkle Root

e686a2a151636928edd9bdf0f6c1e6a5763a913fb3ff1bcbd71f9b637b66c4c0

Transactions (1)

Coinbasee686a2a1516369…1f9b637b66c4c0

1 in → 49 out10.0800 XPM1.69 KB

AKwqFUdz…D4jGNKFN ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC AcMPa5Yh…j5yHgkwm AeJPhjEZ…dkNigEjN

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.

5.630 × 10⁹⁸(99-digit number)

56301846853304130391…10024089089989983999

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

5.630 × 10⁹⁸(99-digit number)

56301846853304130391…10024089089989983999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.630 × 10⁹⁸(99-digit number)

56301846853304130391…10024089089989984001

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

1.126 × 10⁹⁹(100-digit number)

11260369370660826078…20048178179979967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.126 × 10⁹⁹(100-digit number)

11260369370660826078…20048178179979968001

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

2.252 × 10⁹⁹(100-digit number)

22520738741321652156…40096356359959935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.252 × 10⁹⁹(100-digit number)

22520738741321652156…40096356359959936001

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

4.504 × 10⁹⁹(100-digit number)

45041477482643304313…80192712719919871999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.504 × 10⁹⁹(100-digit number)

45041477482643304313…80192712719919872001

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

9.008 × 10⁹⁹(100-digit number)

90082954965286608626…60385425439839743999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.008 × 10⁹⁹(100-digit number)

90082954965286608626…60385425439839744001

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.801 × 10¹⁰⁰(101-digit number)

18016590993057321725…20770850879679487999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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