Block #272,250

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 3:49:57 AM · Difficulty 9.9525 · 6,538,811 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c299d47b83ec37ce11389ec8bd80768ec38a6aa516bca54814b94edfd28065d6

View on Chainz ↗

Height

#272,250

Difficulty

9.952532

Transactions

Size

867 B

Version

Bits

09f3d928

Nonce

104,562

Timestamp

11/25/2013, 3:49:57 AM

Confirmations

6,538,811

Mined by

⛏️ z'aRAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

1b262e92a0bfabc1af54c89933769b31684c14a2032e7b50b7d83e6f82758520

Transactions (1)

Coinbase1b262e92a0bfab…d83e6f82758520

1 in → 21 out10.0800 XPM777 B

APeshfYV…3PKcKMKH APVGazMT…cDCk2nwA Aai6TNLM…kQf2QbQd AUSGA5VC…GYHbnJtz ANuKx9Ke…wm7nrBRq

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.

1.528 × 10⁹⁴(95-digit number)

15284209009811996031…55838787867690595839

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

1.528 × 10⁹⁴(95-digit number)

15284209009811996031…55838787867690595839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.528 × 10⁹⁴(95-digit number)

15284209009811996031…55838787867690595841

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

3.056 × 10⁹⁴(95-digit number)

30568418019623992063…11677575735381191679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.056 × 10⁹⁴(95-digit number)

30568418019623992063…11677575735381191681

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

6.113 × 10⁹⁴(95-digit number)

61136836039247984127…23355151470762383359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.113 × 10⁹⁴(95-digit number)

61136836039247984127…23355151470762383361

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

1.222 × 10⁹⁵(96-digit number)

12227367207849596825…46710302941524766719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.222 × 10⁹⁵(96-digit number)

12227367207849596825…46710302941524766721

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

2.445 × 10⁹⁵(96-digit number)

24454734415699193651…93420605883049533439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.445 × 10⁹⁵(96-digit number)

24454734415699193651…93420605883049533441

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

Block #272,250

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