Block #522,612

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/3/2014, 3:37:39 AM · Difficulty 10.8677 · 6,285,563 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fde7b49da8ecc09fc485be9909da9ca9288e302608e2cad02890a437a3b8a7ff

View on Chainz ↗

Height

#522,612

Difficulty

10.867712

Transactions

Size

17.58 KB

Version

Bits

0ade225e

Nonce

89,936,941

Timestamp

5/3/2014, 3:37:39 AM

Confirmations

6,285,563

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

1f8d8a467406cc9040590e7ee1a1cb68a4787b073485f4fe534f81359b6311bd

Transactions (2)

Coinbase91f5af78ba0a22…d290c74b3d502a

1 in → 1 out8.6318 XPM116 B

AbwWkWZt…kawDhufa

91b7cd7c4cff99…5779d06eb35b25

120 in → 1 out39.8600 XPM17.38 KB

AKHgGrCu…VKhZKef6

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.

4.134 × 10⁹⁸(99-digit number)

41341616968555688897…01370918661048903979

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

4.134 × 10⁹⁸(99-digit number)

41341616968555688897…01370918661048903979

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.134 × 10⁹⁸(99-digit number)

41341616968555688897…01370918661048903981

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

8.268 × 10⁹⁸(99-digit number)

82683233937111377794…02741837322097807959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.268 × 10⁹⁸(99-digit number)

82683233937111377794…02741837322097807961

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

1.653 × 10⁹⁹(100-digit number)

16536646787422275558…05483674644195615919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.653 × 10⁹⁹(100-digit number)

16536646787422275558…05483674644195615921

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

3.307 × 10⁹⁹(100-digit number)

33073293574844551117…10967349288391231839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.307 × 10⁹⁹(100-digit number)

33073293574844551117…10967349288391231841

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

6.614 × 10⁹⁹(100-digit number)

66146587149689102235…21934698576782463679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.614 × 10⁹⁹(100-digit number)

66146587149689102235…21934698576782463681

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

Block #522,612

Cookie Preferences