Block #252,958

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 8:49:05 PM · Difficulty 9.9718 · 6,545,874 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a33c628fdb715ab05487d87abbe9ea9a99001b158a65ddd9c8ea7a2bd9374561

View on Chainz ↗

Height

#252,958

Difficulty

9.971776

Transactions

Size

1.68 KB

Version

Bits

09f8c64b

Nonce

32,575

Timestamp

11/9/2013, 8:49:05 PM

Confirmations

6,545,874

Mined by

⛏️ aR~8AL3P2QDvggde3uU26ZG8H2z2AzgbbaSnCj

Merkle Root

57eb138410e1ad8e04ff6a05921acd724f205394cba3b941d76c60b6e0fa7168

Transactions (1)

Coinbase57eb138410e1ad…6c60b6e0fa7168

1 in → 46 out10.0200 XPM1.59 KB

AL3P2QDv…gbbaSnCj AHUMdCV5…eXnCsijo AWJHU8CF…JUjqyNaX AScCYXya…oAz38X3p AKDTDDtx…iqvw9cdY

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.

3.659 × 10⁹²(93-digit number)

36593674018671642966…18628868368805887999

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

3.659 × 10⁹²(93-digit number)

36593674018671642966…18628868368805887999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.659 × 10⁹²(93-digit number)

36593674018671642966…18628868368805888001

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

7.318 × 10⁹²(93-digit number)

73187348037343285932…37257736737611775999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.318 × 10⁹²(93-digit number)

73187348037343285932…37257736737611776001

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

1.463 × 10⁹³(94-digit number)

14637469607468657186…74515473475223551999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.463 × 10⁹³(94-digit number)

14637469607468657186…74515473475223552001

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

2.927 × 10⁹³(94-digit number)

29274939214937314373…49030946950447103999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.927 × 10⁹³(94-digit number)

29274939214937314373…49030946950447104001

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

5.854 × 10⁹³(94-digit number)

58549878429874628746…98061893900894207999

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