Block #518,708

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/30/2014, 6:47:06 PM · Difficulty 10.8539 · 6,286,380 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1ecc2067117e2eb2a0f52d4008083a69d2bb84b2c739ab235eafa39955d8c466

View on Chainz ↗

Height

#518,708

Difficulty

10.853892

Transactions

Size

1.09 KB

Version

Bits

0ada98a4

Nonce

59,843,293

Timestamp

4/30/2014, 6:47:06 PM

Confirmations

6,286,380

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a0f8295b4b773a6e873e002a5b4d288dc0387e77ad27b7665f85633ad0cb5fbd

Transactions (5)

Coinbase6d21b6332b90c4…e6cc5272b01339

1 in → 1 out8.5100 XPM116 B

AbwWkWZt…kawDhufa

7b7c42ecb722e9…b091184b5c876b

1 in → 2 out5.4547 XPM227 B

AV2yS9JV…DLikvgmf AQ4sGBVL…LTzLzDnu

516d8292934feb…1e67b011be10f3

1 in → 2 out1.7658 XPM226 B

AJmJ6Df6…kNbRvF5i AYziGDCW…XJ5VxbsR

89cfc922326fad…925415063d90e0

1 in → 2 out3.1766 XPM227 B

Aeuc3WSZ…ythjLmc9 AdUeYy7N…CF31vpNt

7c1e8ab7e753b7…e2c75d9cf42134

1 in → 2 out0.6098 XPM227 B

AXYjJpZE…nci6iWsY ATxoEAVm…o1hPnNf4

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.

2.442 × 10⁹⁸(99-digit number)

24422468668414226979…66512328756566330049

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

2.442 × 10⁹⁸(99-digit number)

24422468668414226979…66512328756566330049

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.442 × 10⁹⁸(99-digit number)

24422468668414226979…66512328756566330051

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

4.884 × 10⁹⁸(99-digit number)

48844937336828453959…33024657513132660099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.884 × 10⁹⁸(99-digit number)

48844937336828453959…33024657513132660101

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

9.768 × 10⁹⁸(99-digit number)

97689874673656907919…66049315026265320199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.768 × 10⁹⁸(99-digit number)

97689874673656907919…66049315026265320201

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

1.953 × 10⁹⁹(100-digit number)

19537974934731381583…32098630052530640399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.953 × 10⁹⁹(100-digit number)

19537974934731381583…32098630052530640401

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

3.907 × 10⁹⁹(100-digit number)

39075949869462763167…64197260105061280799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.907 × 10⁹⁹(100-digit number)

39075949869462763167…64197260105061280801

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