Block #265,008

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/19/2013, 4:43:25 AM · Difficulty 9.9634 · 6,530,357 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

41503f5c404e223ea0d7fe115609ab7afc94085856802ef33c4e93fb5b7692dd

View on Chainz ↗

Height

#265,008

Difficulty

9.963404

Transactions

Size

84.30 KB

Version

Bits

09f6a1a8

Nonce

4,446

Timestamp

11/19/2013, 4:43:25 AM

Confirmations

6,530,357

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

43acf4a5536ead32d7e2745e5f2679860e520d0fc2fc4f723b9230b88804e865

Transactions (3)

Coinbase1c30ea6cfe7268…566b4280e1276c

1 in → 2 out10.9300 XPM142 B

AdGRRh1e…QmctLb24 AKNbfPoc…jfkpwAyL

df75afc513313a…bdf3898ea56d7c

33 in → 1 out401.1222 XPM4.81 KB

AUgqjYtv…yZksNPx7

bd94038b70707c…2551941e6bf8c6

548 in → 2 out25.0100 XPM79.26 KB

AJ3BPx1X…bj3p7KDS ASkvv2MG…NXzJys2L

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.

2.426 × 10⁹⁵(96-digit number)

24269637390091841127…49140255165382865839

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

2.426 × 10⁹⁵(96-digit number)

24269637390091841127…49140255165382865839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.426 × 10⁹⁵(96-digit number)

24269637390091841127…49140255165382865841

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

4.853 × 10⁹⁵(96-digit number)

48539274780183682254…98280510330765731679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.853 × 10⁹⁵(96-digit number)

48539274780183682254…98280510330765731681

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

9.707 × 10⁹⁵(96-digit number)

97078549560367364509…96561020661531463359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.707 × 10⁹⁵(96-digit number)

97078549560367364509…96561020661531463361

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

1.941 × 10⁹⁶(97-digit number)

19415709912073472901…93122041323062926719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.941 × 10⁹⁶(97-digit number)

19415709912073472901…93122041323062926721

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

3.883 × 10⁹⁶(97-digit number)

38831419824146945803…86244082646125853439

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