Block #265,390

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/19/2013, 12:50:32 PM · Difficulty 9.9627 · 6,564,966 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

245e54a42ff62afa3b5923650fce6c26e6b7cc1510e790564197774f28272d57

View on Chainz ↗

Height

#265,390

Difficulty

9.962655

Transactions

Size

2.70 KB

Version

Bits

09f67097

Nonce

8,010

Timestamp

11/19/2013, 12:50:32 PM

Confirmations

6,564,966

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

6e2881a1e4c846f70e4dbc190e29af3796b5922d631a01873d60bf3ef030287b

Transactions (5)

Coinbase38ec9d21d29d36…bc2435bf8f0325

1 in → 2 out10.1000 XPM137 B

AKcbk49N…GJbKa7j1 AU6kq4CL…dQBLvxLp

b0dd2d48e48d80…6e4218fb8eb2f3

6 in → 2 out579.3814 XPM964 B

AdJ94RFC…gpZowzjd AappvufJ…tzXbeoVL

01eb6ee2106672…ada4eedf1c2a95

4 in → 2 out49.5126 XPM670 B

AZY4gEV2…CBRScua7 AdJ94RFC…gpZowzjd

b12f17dbc6d5cb…276466c7a0e128

4 in → 2 out274.9101 XPM672 B

AStEjmeQ…sCirM2Z2 ATP6ihBz…va7MpWW8

50b51c379cf665…68b02560e360ad

1 in → 2 out8.0080 XPM227 B

AJg88wYq…WAcJ6g6B AVC4o9v9…qLxb8oqT

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.

3.551 × 10⁹⁴(95-digit number)

35511251540901925021…06913236437221948439

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

3.551 × 10⁹⁴(95-digit number)

35511251540901925021…06913236437221948439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.551 × 10⁹⁴(95-digit number)

35511251540901925021…06913236437221948441

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

7.102 × 10⁹⁴(95-digit number)

71022503081803850042…13826472874443896879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.102 × 10⁹⁴(95-digit number)

71022503081803850042…13826472874443896881

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

1.420 × 10⁹⁵(96-digit number)

14204500616360770008…27652945748887793759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.420 × 10⁹⁵(96-digit number)

14204500616360770008…27652945748887793761

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

2.840 × 10⁹⁵(96-digit number)

28409001232721540016…55305891497775587519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.840 × 10⁹⁵(96-digit number)

28409001232721540016…55305891497775587521

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

5.681 × 10⁹⁵(96-digit number)

56818002465443080033…10611782995551175039

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 #265,390

Cookie Preferences