Block #272,763

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 10:51:30 AM · Difficulty 9.9534 · 6,554,319 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0571e28e815ec7a79a80fd8d5a2727f0b6255c51ed1229d3aec19ae354b1cb73

View on Chainz ↗

Height

#272,763

Difficulty

9.953399

Transactions

Size

1.72 KB

Version

Bits

09f411f9

Nonce

29,381

Timestamp

11/25/2013, 10:51:30 AM

Confirmations

6,554,319

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

63fbd8fe14489661f63f05bed664085ba0a12f5c2afffa38b2525ebcab2e7098

Transactions (4)

Coinbase80abcfc7af8cf8…5fa9040994a7b2

1 in → 2 out10.1100 XPM142 B

AdGRRh1e…QmctLb24 AKNbfPoc…jfkpwAyL

cfc96c892fa438…9a7ef27e4bf8b5

3 in → 2 out50.0102 XPM522 B

AVurKAnj…hWqRuymR ALBLgM7t…9bQpfaND

096be703b94431…059d907e5645c2

5 in → 2 out49.5158 XPM815 B

AevVoWTS…xgHZWRec AbxQn5nH…4vJ53m4U

fa74b62eb7a7d8…1d451afca89d1b

1 in → 1 out2.9956 XPM193 B

ANX1YLsv…GReXDPhr

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.

3.540 × 10¹⁰³(104-digit number)

35406129498896864300…65356385939578131999

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

3.540 × 10¹⁰³(104-digit number)

35406129498896864300…65356385939578131999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.540 × 10¹⁰³(104-digit number)

35406129498896864300…65356385939578132001

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

7.081 × 10¹⁰³(104-digit number)

70812258997793728600…30712771879156263999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.081 × 10¹⁰³(104-digit number)

70812258997793728600…30712771879156264001

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

1.416 × 10¹⁰⁴(105-digit number)

14162451799558745720…61425543758312527999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.416 × 10¹⁰⁴(105-digit number)

14162451799558745720…61425543758312528001

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

2.832 × 10¹⁰⁴(105-digit number)

28324903599117491440…22851087516625055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.832 × 10¹⁰⁴(105-digit number)

28324903599117491440…22851087516625056001

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

5.664 × 10¹⁰⁴(105-digit number)

56649807198234982880…45702175033250111999

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 #272,763

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