Block #89,205

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/30/2013, 5:02:27 AM · Difficulty 9.2603 · 6,716,710 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6fd36e5e7e537782a122eeb3b9790d170013bbad17b48158168afd86ba629184

View on Chainz ↗

Height

#89,205

Difficulty

9.260340

Transactions

Size

3.57 KB

Version

Bits

0942a59d

Nonce

774

Timestamp

7/30/2013, 5:02:27 AM

Confirmations

6,716,710

Mined by

⛏️ P2SHAanZdGsBmQ7ZvvoNLY1M2cxa9Zht6jRCUw

Merkle Root

88f4faee11162146a8476e612ac35dde0e80e2a63a72fbdabe0fd549d6bbc2d4

Transactions (5)

Coinbaseaa685d4dad5caf…55ee0418b08fa0

1 in → 1 out11.6900 XPM110 B

AanZdGsB…ht6jRCUw

85f421eefe9ed5…c767d9f53225b3

6 in → 2 out138.5094 XPM967 B

AeX25w4W…s73UHntz AWyyoive…djdytvo9

3aeae4eef37c8d…a8038cbb4689d5

3 in → 2 out111.1174 XPM521 B

AQxxh1sE…1tC7pAiz AWyyoive…djdytvo9

30fd41e361e0db…2b8b448bad4496

14 in → 2 out139.0400 XPM1.71 KB

AWYdw6oE…ZNwrDbFX AJc7ETo3…y5s7mhvH

4d455421909b30…b1be736311e15a

1 in → 2 out3.4633 XPM225 B

AT5ycVwC…4eYdjAcx AcjxnR7X…gTPXqpNJ

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.

8.398 × 10⁹⁷(98-digit number)

83982394666696858170…38340364349034152649

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

8.398 × 10⁹⁷(98-digit number)

83982394666696858170…38340364349034152649

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.398 × 10⁹⁷(98-digit number)

83982394666696858170…38340364349034152651

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

1.679 × 10⁹⁸(99-digit number)

16796478933339371634…76680728698068305299

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.679 × 10⁹⁸(99-digit number)

16796478933339371634…76680728698068305301

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

3.359 × 10⁹⁸(99-digit number)

33592957866678743268…53361457396136610599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.359 × 10⁹⁸(99-digit number)

33592957866678743268…53361457396136610601

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

6.718 × 10⁹⁸(99-digit number)

67185915733357486536…06722914792273221199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.718 × 10⁹⁸(99-digit number)

67185915733357486536…06722914792273221201

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

1.343 × 10⁹⁹(100-digit number)

13437183146671497307…13445829584546442399

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