Block #566,930

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/29/2014, 8:48:08 AM · Difficulty 10.9651 · 6,243,035 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8ee1ff545a91218425e14a5bb4f7e9fc71eb7131ce9517cbbfb3637c020bad67

View on Chainz ↗

Height

#566,930

Difficulty

10.965071

Transactions

Size

1.29 KB

Version

Bits

0af70eed

Nonce

2,160,808,739

Timestamp

5/29/2014, 8:48:08 AM

Confirmations

6,243,035

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ee0893266ef94c770e68e246cb60b1918237a33007bd072cb157debc57175301

Transactions (2)

Coinbased98ccd29e57f64…d2b265aece71aa

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

353656db768a2f…3d17be5585e5fc

7 in → 2 out181.0100 XPM1.09 KB

AWysc2z7…wYfkWNbe AZkeEsRz…YNALnwzA

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.

5.634 × 10⁹⁷(98-digit number)

56341890027230820480…44552421690831884159

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

5.634 × 10⁹⁷(98-digit number)

56341890027230820480…44552421690831884159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.634 × 10⁹⁷(98-digit number)

56341890027230820480…44552421690831884161

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

1.126 × 10⁹⁸(99-digit number)

11268378005446164096…89104843381663768319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.126 × 10⁹⁸(99-digit number)

11268378005446164096…89104843381663768321

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

2.253 × 10⁹⁸(99-digit number)

22536756010892328192…78209686763327536639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.253 × 10⁹⁸(99-digit number)

22536756010892328192…78209686763327536641

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

4.507 × 10⁹⁸(99-digit number)

45073512021784656384…56419373526655073279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.507 × 10⁹⁸(99-digit number)

45073512021784656384…56419373526655073281

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

9.014 × 10⁹⁸(99-digit number)

90147024043569312768…12838747053310146559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.014 × 10⁹⁸(99-digit number)

90147024043569312768…12838747053310146561

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.802 × 10⁹⁹(100-digit number)

18029404808713862553…25677494106620293119

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #566,930

Cookie Preferences