Block #252,672

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 5:17:57 PM · Difficulty 9.9713 · 6,537,114 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

91e280f0541cc67ea9d62b0d35e2f7110b7989a1dfb0bf71a71c183da196195f

View on Chainz ↗

Height

#252,672

Difficulty

9.971346

Transactions

Size

1.47 KB

Version

Bits

09f8aa1e

Nonce

8,196

Timestamp

11/9/2013, 5:17:57 PM

Confirmations

6,537,114

Merkle Root

5d9647ef42d3553f5df8c44253aad7c20ffc4083d8170bcd46f3a78b2160bccd

Transactions (4)

Coinbaseb1ae5803d95ff1…b2b71cb5c1a539

1 in → 2 out10.0700 XPM142 B

AKcbk49N…GJbKa7j1 Abiw8n3q…ZnZfgvQW

3fccdffbe1dfbb…7fa442d523602b

4 in → 2 out227.2083 XPM671 B

AdGYnqoY…pjMuwV34 Ac4S2NQt…Lgev9Ake

a98185b29f0df1…ef7c25b4284c1b

2 in → 2 out13.0342 XPM374 B

AKscBEzU…Yu9M6xqh ASuoUi24…FwBoFbxd

7e82d7d3647939…6d3dec6b921962

1 in → 2 out0.9900 XPM227 B

AdRre6fW…pTJDVQk6 ARjqnoYd…FsP3c6ZD

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.

5.825 × 10⁹⁶(97-digit number)

58253369618318069683…08862904797541678079

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

5.825 × 10⁹⁶(97-digit number)

58253369618318069683…08862904797541678079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.825 × 10⁹⁶(97-digit number)

58253369618318069683…08862904797541678081

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

1.165 × 10⁹⁷(98-digit number)

11650673923663613936…17725809595083356159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.165 × 10⁹⁷(98-digit number)

11650673923663613936…17725809595083356161

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

2.330 × 10⁹⁷(98-digit number)

23301347847327227873…35451619190166712319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.330 × 10⁹⁷(98-digit number)

23301347847327227873…35451619190166712321

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

4.660 × 10⁹⁷(98-digit number)

46602695694654455747…70903238380333424639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.660 × 10⁹⁷(98-digit number)

46602695694654455747…70903238380333424641

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

9.320 × 10⁹⁷(98-digit number)

93205391389308911494…41806476760666849279

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