Block #297,771

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/6/2013, 7:42:52 PM · Difficulty 9.9920 · 6,508,295 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ec9851bd6c64e3932ade76326964429a292e0395e3301441ac6d0c3c55bcd5b6

View on Chainz ↗

Height

#297,771

Difficulty

9.992047

Transactions

Size

1.11 KB

Version

Bits

09fdf6c5

Nonce

284,030

Timestamp

12/6/2013, 7:42:52 PM

Confirmations

6,508,295

Mined by

⛏️ +aRARzXge7STrHg8ZTMRW57MCNAWRCEjL5oYm

Merkle Root

2f030584f7d7c6e1f735a99027fd1bffd50a0272f9fedfc5db1dcfb844952b94

Transactions (1)

Coinbase2f030584f7d7c6…1dcfb844952b94

1 in → 29 out9.9800 XPM1.02 KB

ARzXge7S…CEjL5oYm AYtDvcGs…VuAcA7m7 AHuJ9wYh…BGmgHrKZ AWXYBWKP…qQAoisBJ AYcLTeXR…bscgPops

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.

1.332 × 10⁹⁵(96-digit number)

13328708332231797150…11279882291235629999

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

1.332 × 10⁹⁵(96-digit number)

13328708332231797150…11279882291235629999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.332 × 10⁹⁵(96-digit number)

13328708332231797150…11279882291235630001

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

2.665 × 10⁹⁵(96-digit number)

26657416664463594300…22559764582471259999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.665 × 10⁹⁵(96-digit number)

26657416664463594300…22559764582471260001

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

5.331 × 10⁹⁵(96-digit number)

53314833328927188600…45119529164942519999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.331 × 10⁹⁵(96-digit number)

53314833328927188600…45119529164942520001

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

1.066 × 10⁹⁶(97-digit number)

10662966665785437720…90239058329885039999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.066 × 10⁹⁶(97-digit number)

10662966665785437720…90239058329885040001

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

2.132 × 10⁹⁶(97-digit number)

21325933331570875440…80478116659770079999

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