Block #265,364

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/19/2013, 12:11:21 PM · Difficulty 9.9627 · 6,530,000 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5d86e18de20dd540b6181ead3e61653efef0c4a7c6c9d67a96ad819343e6f16f

View on Chainz ↗

Height

#265,364

Difficulty

9.962746

Transactions

Size

2.54 KB

Version

Bits

09f67687

Nonce

24,181

Timestamp

11/19/2013, 12:11:21 PM

Confirmations

6,530,000

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

ba99136ad3aa0475c90cc207b19d0572f5e04cc287b2671c2819d9c7c2a5d80d

Transactions (3)

Coinbase7c949524a618a1…5ebec25c5e35da

1 in → 2 out10.1000 XPM136 B

AKcbk49N…GJbKa7j1 AHsw4d6U…EnM8UXNZ

869910370f3072…a4f947d5bb9727

8 in → 2 out2390.4332 XPM1.23 KB

AXgoyaZE…UMFu7gxX AMXNys2D…arsKrv3M

87a0670a400f56…25ecfecd4053f9

7 in → 2 out70.3300 XPM1.09 KB

ANcwFtw9…18HQhgoZ AYo8Zs3r…cgLJj8rx

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.

4.080 × 10⁹⁵(96-digit number)

40805562556350330463…57354708021527925919

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

4.080 × 10⁹⁵(96-digit number)

40805562556350330463…57354708021527925919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.080 × 10⁹⁵(96-digit number)

40805562556350330463…57354708021527925921

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

8.161 × 10⁹⁵(96-digit number)

81611125112700660927…14709416043055851839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.161 × 10⁹⁵(96-digit number)

81611125112700660927…14709416043055851841

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

1.632 × 10⁹⁶(97-digit number)

16322225022540132185…29418832086111703679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.632 × 10⁹⁶(97-digit number)

16322225022540132185…29418832086111703681

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

3.264 × 10⁹⁶(97-digit number)

32644450045080264370…58837664172223407359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.264 × 10⁹⁶(97-digit number)

32644450045080264370…58837664172223407361

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

6.528 × 10⁹⁶(97-digit number)

65288900090160528741…17675328344446814719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.528 × 10⁹⁶(97-digit number)

65288900090160528741…17675328344446814721

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