Block #269,451

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 4:04:31 AM · Difficulty 9.9531 · 6,525,274 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5c5037de0c3d3d3e110fdd488f62d36ffcbb83ac1f83ab7ca0be1110e9eb6ecf

View on Chainz ↗

Height

#269,451

Difficulty

9.953060

Transactions

Size

56.52 KB

Version

Bits

09f3fbbe

Nonce

232,147

Timestamp

11/23/2013, 4:04:31 AM

Confirmations

6,525,274

Mined by

⛏️ P2SHAKZRTeibCRPJERy8tcoXfcgXLaYRKZ5TxW

Merkle Root

724198c4bfdeeb65156560580e4257105f4fc23312d233af662d1d84ac0bcd17

Transactions (5)

Coinbase39bd34cb049334…21759d0202fe44

1 in → 1 out10.7300 XPM109 B

AKZRTeib…YRKZ5TxW

956425aeb5d37a…d42bb66fe2c0dd

4 in → 2 out471.7728 XPM672 B

AMp932er…YKafDQoo AZd9MT9j…5jj5HB1f

409f1c3fb9b379…afbfcf61c22001

343 in → 2 out100.0100 XPM49.62 KB

AW5ZG6uT…zvVxpna1 AWqaTsc3…gvPMMZMm

ea06baf54c8a63…ff4ab1afead6f3

3 in → 2 out4.0300 XPM522 B

ALH1eWNc…VYqCNwwu AUj6vtXm…QVanfMYa

533090f23d324a…b431fa5b869c39

38 in → 1 out8.8587 XPM5.53 KB

Acy5hWbh…uFhC2Yj9

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.

3.246 × 10⁹¹(92-digit number)

32467909363141164912…81360109347465572489

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

3.246 × 10⁹¹(92-digit number)

32467909363141164912…81360109347465572489

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.246 × 10⁹¹(92-digit number)

32467909363141164912…81360109347465572491

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

6.493 × 10⁹¹(92-digit number)

64935818726282329825…62720218694931144979

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.493 × 10⁹¹(92-digit number)

64935818726282329825…62720218694931144981

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

1.298 × 10⁹²(93-digit number)

12987163745256465965…25440437389862289959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.298 × 10⁹²(93-digit number)

12987163745256465965…25440437389862289961

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

2.597 × 10⁹²(93-digit number)

25974327490512931930…50880874779724579919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.597 × 10⁹²(93-digit number)

25974327490512931930…50880874779724579921

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

5.194 × 10⁹²(93-digit number)

51948654981025863860…01761749559449159839

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