Block #497,195

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/17/2014, 11:33:43 AM · Difficulty 10.7643 · 6,301,232 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

98ce9fc32c910177df48f51ea814f0777e97d041b99401f74388f57d8067f31f

View on Chainz ↗

Height

#497,195

Difficulty

10.764292

Transactions

Size

17.48 KB

Version

Bits

0ac3a89d

Nonce

39,026,473

Timestamp

4/17/2014, 11:33:43 AM

Confirmations

6,301,232

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

becf2d756896e33411d9511f4e5c70ca43fdd5088fb37705720685fa8b1ba660

Transactions (4)

Coinbasef3c50cb1b39cb7…9503be89c24cc5

1 in → 1 out8.8200 XPM116 B

AbwWkWZt…kawDhufa

cbe1b05993db9a…94b700bb695a8f

115 in → 2 out500.0101 XPM16.70 KB

AZiHBZXe…YFC1QDwT AJjnK9uC…VreFquR4

fe3803bf7dfe52…9383abd7734eba

1 in → 2 out2.5965 XPM225 B

AQhSMLqz…ZR5BbvZ9 AWdMXbni…KfsUmYuQ

4136e1a4ebca8b…44800d78d1f265

2 in → 2 out1.1701 XPM375 B

AG8u7ddV…cU5QJSqk AHMEp86h…17xzgfNx

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.

5.648 × 10⁹⁸(99-digit number)

56488158232885901321…13574633328333816959

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

5.648 × 10⁹⁸(99-digit number)

56488158232885901321…13574633328333816959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.648 × 10⁹⁸(99-digit number)

56488158232885901321…13574633328333816961

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

1.129 × 10⁹⁹(100-digit number)

11297631646577180264…27149266656667633919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.129 × 10⁹⁹(100-digit number)

11297631646577180264…27149266656667633921

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

2.259 × 10⁹⁹(100-digit number)

22595263293154360528…54298533313335267839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.259 × 10⁹⁹(100-digit number)

22595263293154360528…54298533313335267841

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

4.519 × 10⁹⁹(100-digit number)

45190526586308721057…08597066626670535679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.519 × 10⁹⁹(100-digit number)

45190526586308721057…08597066626670535681

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

9.038 × 10⁹⁹(100-digit number)

90381053172617442114…17194133253341071359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.038 × 10⁹⁹(100-digit number)

90381053172617442114…17194133253341071361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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