Block #268,093

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/21/2013, 8:02:55 PM · Difficulty 9.9580 · 6,544,743 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a61e56e0b7932895d2a387785fd110aea96524091553bdc73e3e1e562b69d0ec

View on Chainz ↗

Height

#268,093

Difficulty

9.957958

Transactions

Size

2.04 KB

Version

Bits

09f53cc3

Nonce

20,847

Timestamp

11/21/2013, 8:02:55 PM

Confirmations

6,544,743

Mined by

⛏️ =aRfAFuakYLnxFs7PgaWe4P452CULexnY8QBEG

Merkle Root

646629a48d6b51df36742c597fd4eb0a8cb5680ae892834dce64bb651286c4ac

Transactions (1)

Coinbase646629a48d6b51…64bb651286c4ac

1 in → 57 out10.0500 XPM1.95 KB

AFuakYLn…xnY8QBEG AKXeSXzu…yeuNjvhB ANuKx9Ke…wm7nrBRq ANHbaxZp…XjnHCJJs AVzhvfTX…ZzNJYq61

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.

2.163 × 10⁹⁵(96-digit number)

21632563203851188105…46628504028854970239

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

2.163 × 10⁹⁵(96-digit number)

21632563203851188105…46628504028854970239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.163 × 10⁹⁵(96-digit number)

21632563203851188105…46628504028854970241

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

4.326 × 10⁹⁵(96-digit number)

43265126407702376210…93257008057709940479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.326 × 10⁹⁵(96-digit number)

43265126407702376210…93257008057709940481

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

8.653 × 10⁹⁵(96-digit number)

86530252815404752421…86514016115419880959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.653 × 10⁹⁵(96-digit number)

86530252815404752421…86514016115419880961

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

1.730 × 10⁹⁶(97-digit number)

17306050563080950484…73028032230839761919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.730 × 10⁹⁶(97-digit number)

17306050563080950484…73028032230839761921

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

3.461 × 10⁹⁶(97-digit number)

34612101126161900968…46056064461679523839

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 #268,093

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