Block #272,910

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 12:55:30 PM · Difficulty 9.9536 · 6,526,399 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

48c6990f9529be046ae1721acf2cf8d0d2fa5a4089f1f0dcf4795d66b6dc7559

View on Chainz ↗

Height

#272,910

Difficulty

9.953617

Transactions

Size

1.08 KB

Version

Bits

09f4203c

Nonce

202,535

Timestamp

11/25/2013, 12:55:30 PM

Confirmations

6,526,399

Mined by

⛏️ *aRHAb3J4ipopCDiBmuX9CWCummQr4GaHrWuuW

Merkle Root

1e7e9f2b6b0c4c81a935ce70ec265a0e0cef01cc4cfca603676f986b64426331

Transactions (1)

Coinbase1e7e9f2b6b0c4c…6f986b64426331

1 in → 28 out10.0600 XPM1015 B

Ab3J4ipo…GaHrWuuW APeshfYV…3PKcKMKH AQyr8Lw3…hs4nt3Pn ALdHh27b…XNbqrvPf Ac5sZcdP…kzV4eckG

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.

3.508 × 10⁹⁶(97-digit number)

35086401821601070899…55120230869498711999

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

3.508 × 10⁹⁶(97-digit number)

35086401821601070899…55120230869498711999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.508 × 10⁹⁶(97-digit number)

35086401821601070899…55120230869498712001

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

7.017 × 10⁹⁶(97-digit number)

70172803643202141798…10240461738997423999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.017 × 10⁹⁶(97-digit number)

70172803643202141798…10240461738997424001

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

1.403 × 10⁹⁷(98-digit number)

14034560728640428359…20480923477994847999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.403 × 10⁹⁷(98-digit number)

14034560728640428359…20480923477994848001

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

2.806 × 10⁹⁷(98-digit number)

28069121457280856719…40961846955989695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.806 × 10⁹⁷(98-digit number)

28069121457280856719…40961846955989696001

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

5.613 × 10⁹⁷(98-digit number)

56138242914561713438…81923693911979391999

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