Block #272,500

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 7:10:20 AM · Difficulty 9.9530 · 6,529,716 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

209a3f51ac5bd75dec5b6120f48933543bb42343d62057ab9b7f6a17c550a777

View on Chainz ↗

Height

#272,500

Difficulty

9.953011

Transactions

Size

900 B

Version

Bits

09f3f882

Nonce

449,575

Timestamp

11/25/2013, 7:10:20 AM

Confirmations

6,529,716

Mined by

⛏️ tAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

b07ae29ffaeeb7290de9ce3ae9d703c3c8eeb4d0f60c49d092705296935d5627

Transactions (1)

Coinbaseb07ae29ffaeeb7…705296935d5627

1 in → 22 out10.0800 XPM811 B

APeshfYV…3PKcKMKH ALFWpHxd…zhX7LjhL Aecydusm…h94ozF4E Aai6TNLM…kQf2QbQd AMR89gp5…oZEXFX4Z

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.

7.086 × 10⁹²(93-digit number)

70865983014340818355…61471177024745921279

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

7.086 × 10⁹²(93-digit number)

70865983014340818355…61471177024745921279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.086 × 10⁹²(93-digit number)

70865983014340818355…61471177024745921281

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

1.417 × 10⁹³(94-digit number)

14173196602868163671…22942354049491842559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.417 × 10⁹³(94-digit number)

14173196602868163671…22942354049491842561

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

2.834 × 10⁹³(94-digit number)

28346393205736327342…45884708098983685119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.834 × 10⁹³(94-digit number)

28346393205736327342…45884708098983685121

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

5.669 × 10⁹³(94-digit number)

56692786411472654684…91769416197967370239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.669 × 10⁹³(94-digit number)

56692786411472654684…91769416197967370241

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

1.133 × 10⁹⁴(95-digit number)

11338557282294530936…83538832395934740479

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