Block #182,183

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/27/2013, 2:57:04 AM · Difficulty 9.8590 · 6,625,162 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

882b9e66fb3970c41214ddbd06b3ee0e32a7126f6288a125849078e5ecc79090

View on Chainz ↗

Height

#182,183

Difficulty

9.859029

Transactions

Size

538 B

Version

Bits

09dbe959

Nonce

968,175

Timestamp

9/27/2013, 2:57:04 AM

Confirmations

6,625,162

Mined by

⛏️ P2SHAHQYURELytohHd9LBineG3ukvCLv1QqWNV

Merkle Root

6b745d01e5dac18e067dcd90b82c8a21e62a75f638052dddfbfbfa28f4db59ad

Transactions (2)

Coinbase71385c81356f96…edc70315d543eb

1 in → 1 out10.2800 XPM109 B

AHQYUREL…Lv1QqWNV

ab0182ef372685…9769a12c7d101e

2 in → 1 out30.7600 XPM340 B

AbEVNHvT…4XP8UPJZ

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.

1.172 × 10⁹³(94-digit number)

11721288985659706674…95932064091524289359

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

1.172 × 10⁹³(94-digit number)

11721288985659706674…95932064091524289359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.172 × 10⁹³(94-digit number)

11721288985659706674…95932064091524289361

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

2.344 × 10⁹³(94-digit number)

23442577971319413348…91864128183048578719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.344 × 10⁹³(94-digit number)

23442577971319413348…91864128183048578721

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

4.688 × 10⁹³(94-digit number)

46885155942638826697…83728256366097157439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.688 × 10⁹³(94-digit number)

46885155942638826697…83728256366097157441

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

9.377 × 10⁹³(94-digit number)

93770311885277653395…67456512732194314879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.377 × 10⁹³(94-digit number)

93770311885277653395…67456512732194314881

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

1.875 × 10⁹⁴(95-digit number)

18754062377055530679…34913025464388629759

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 #182,183

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