Block #272,595

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 8:34:07 AM · Difficulty 9.9531 · 6,543,344 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ac25fbdfc17fe721781312f766160a8d4ed7c10bbd861e47247af95927ea86d7

View on Chainz ↗

Height

#272,595

Difficulty

9.953129

Transactions

Size

1.01 KB

Version

Bits

09f40040

Nonce

61,058

Timestamp

11/25/2013, 8:34:07 AM

Confirmations

6,543,344

Mined by

⛏️ aRANQKf2g4DxZYfvtufGHqF2cNQk29NaVj23

Merkle Root

3ea1c83cfe920c278f8c21aa64a82baacc9ee558f93ba05cfc844516efa42aaf

Transactions (1)

Coinbase3ea1c83cfe920c…844516efa42aaf

1 in → 26 out10.0800 XPM947 B

ANQKf2g4…29NaVj23 AQyr8Lw3…hs4nt3Pn Aaf3CsqS…k1Eu3vmJ Ac9ofGgC…KaPzHH7W AYJroGmH…JhmajDzq

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.

2.594 × 10⁹⁷(98-digit number)

25949148242890603141…15389734818728878079

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

2.594 × 10⁹⁷(98-digit number)

25949148242890603141…15389734818728878079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.594 × 10⁹⁷(98-digit number)

25949148242890603141…15389734818728878081

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

5.189 × 10⁹⁷(98-digit number)

51898296485781206283…30779469637457756159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.189 × 10⁹⁷(98-digit number)

51898296485781206283…30779469637457756161

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

1.037 × 10⁹⁸(99-digit number)

10379659297156241256…61558939274915512319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.037 × 10⁹⁸(99-digit number)

10379659297156241256…61558939274915512321

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

2.075 × 10⁹⁸(99-digit number)

20759318594312482513…23117878549831024639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.075 × 10⁹⁸(99-digit number)

20759318594312482513…23117878549831024641

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

4.151 × 10⁹⁸(99-digit number)

41518637188624965026…46235757099662049279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.151 × 10⁹⁸(99-digit number)

41518637188624965026…46235757099662049281

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 #272,595

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