Block #182,511

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/27/2013, 8:59:52 AM · Difficulty 9.8580 · 6,625,062 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8e65fb7470c08aea7646385d32c40559bb830b5c95a1695be94430318df6c288

View on Chainz ↗

Height

#182,511

Difficulty

9.858037

Transactions

Size

2.23 KB

Version

Bits

09dba848

Nonce

167,774

Timestamp

9/27/2013, 8:59:52 AM

Confirmations

6,625,062

Mined by

⛏️ P2SHAT3dRckguQx6f5eEEVjWX7iYBwiggfceho

Merkle Root

a17416e5f94c4346d7d33934a24b76d0b95458814d4e31b0114779a9fed5e171

Transactions (5)

Coinbase362e710a711905…5d559c923e4255

1 in → 1 out10.3200 XPM109 B

AT3dRckg…iggfceho

b84dba95903f95…2b9a962852d586

1 in → 2 out10.2500 XPM225 B

AWp8Bq4X…6g9ycwCu AM2AgJ4m…EAV4s5r2

90bd308498963c…38d0b042b7f95f

2 in → 2 out20.5100 XPM376 B

AetJMA4s…LT3f8bBh AbwTU8Vc…LznXZEgd

5a8a1c49be36f6…adbf311b69faaa

8 in → 2 out50.0368 XPM1.23 KB

ATx7J3QS…CyXUcpwB AeNN5j6e…kwdNtNKX

5c71dac40c4a61…82172aa131c883

1 in → 2 out8.1648 XPM225 B

AcuM7XiJ…5uND8Jce AUmpu8v8…NfmxvUSM

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.

4.496 × 10⁹⁰(91-digit number)

44963821486324951209…67901967161216262399

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

4.496 × 10⁹⁰(91-digit number)

44963821486324951209…67901967161216262399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.496 × 10⁹⁰(91-digit number)

44963821486324951209…67901967161216262401

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

8.992 × 10⁹⁰(91-digit number)

89927642972649902418…35803934322432524799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.992 × 10⁹⁰(91-digit number)

89927642972649902418…35803934322432524801

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

1.798 × 10⁹¹(92-digit number)

17985528594529980483…71607868644865049599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.798 × 10⁹¹(92-digit number)

17985528594529980483…71607868644865049601

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

3.597 × 10⁹¹(92-digit number)

35971057189059960967…43215737289730099199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.597 × 10⁹¹(92-digit number)

35971057189059960967…43215737289730099201

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

7.194 × 10⁹¹(92-digit number)

71942114378119921934…86431474579460198399

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

Block #182,511

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