Block #188,082

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/30/2013, 11:26:35 PM · Difficulty 9.8693 · 6,622,445 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

49fbeec29242d66b2f7485b0b48dcd5ada83b5cbb2e4442c14521ab496a1b049

View on Chainz ↗

Height

#188,082

Difficulty

9.869313

Transactions

Size

651 B

Version

Bits

09de8b4b

Nonce

37,774

Timestamp

9/30/2013, 11:26:35 PM

Confirmations

6,622,445

Mined by

⛏️ P2SHASYrYisDdLkc429RY8uvn73FVJokXVUDVb

Merkle Root

81035f90bc224aade6e91f7db316e229b96eddb50f63d9e3cfbd135a319a6885

Transactions (3)

Coinbase85a49431546bd0…1ceec12679ec9f

1 in → 1 out10.2700 XPM109 B

ASYrYisD…okXVUDVb

f128f3d344dfd6…db9baeeddfc4bf

1 in → 2 out10.2600 XPM226 B

AMuHoUJM…uk76LdKE AVTssqMN…ajDfdPmP

f5e78679524aa5…c50c8f948586e2

1 in → 2 out10.2600 XPM227 B

ALkVzNFi…6szjyZfb AYY57m9r…88jd5CHg

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.

4.399 × 10⁹¹(92-digit number)

43993891113746480977…56227583828212025159

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

4.399 × 10⁹¹(92-digit number)

43993891113746480977…56227583828212025159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.399 × 10⁹¹(92-digit number)

43993891113746480977…56227583828212025161

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

8.798 × 10⁹¹(92-digit number)

87987782227492961954…12455167656424050319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.798 × 10⁹¹(92-digit number)

87987782227492961954…12455167656424050321

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

1.759 × 10⁹²(93-digit number)

17597556445498592390…24910335312848100639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.759 × 10⁹²(93-digit number)

17597556445498592390…24910335312848100641

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

3.519 × 10⁹²(93-digit number)

35195112890997184781…49820670625696201279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.519 × 10⁹²(93-digit number)

35195112890997184781…49820670625696201281

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

7.039 × 10⁹²(93-digit number)

70390225781994369563…99641341251392402559

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 #188,082

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