Block #566,725

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/29/2014, 3:01:14 AM · Difficulty 10.9660 · 6,260,580 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

307fff4b9512ebc0bfd9862510fd5f4bd430b5b0eceaf4f6df0d31bde265869b

View on Chainz ↗

Height

#566,725

Difficulty

10.966046

Transactions

Size

659 B

Version

Bits

0af74ece

Nonce

1,438,392,876

Timestamp

5/29/2014, 3:01:14 AM

Confirmations

6,260,580

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

bc66b3af1a9a3c0764f78ca1355f939109d16c854959bb214830e973a26b9a7e

Transactions (3)

Coinbasecd8c3bf280b34b…1b23bfb70d576b

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

2211f752f9fe35…7151fb557e0d80

1 in → 2 out6.2632 XPM225 B

ALBvx18W…PmjyqcLv AZcbtVdK…DBQpQGv2

b7f6d85963eb75…537ec6c44a233f

1 in → 2 out3.1657 XPM227 B

AGwmkokc…pU1eN47k Ae9WKRtS…hXwjxAw5

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.

1.285 × 10⁹⁷(98-digit number)

12859570042281936487…68412889061361893739

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

1.285 × 10⁹⁷(98-digit number)

12859570042281936487…68412889061361893739

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.285 × 10⁹⁷(98-digit number)

12859570042281936487…68412889061361893741

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

2.571 × 10⁹⁷(98-digit number)

25719140084563872975…36825778122723787479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.571 × 10⁹⁷(98-digit number)

25719140084563872975…36825778122723787481

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

5.143 × 10⁹⁷(98-digit number)

51438280169127745951…73651556245447574959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.143 × 10⁹⁷(98-digit number)

51438280169127745951…73651556245447574961

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

1.028 × 10⁹⁸(99-digit number)

10287656033825549190…47303112490895149919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.028 × 10⁹⁸(99-digit number)

10287656033825549190…47303112490895149921

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

2.057 × 10⁹⁸(99-digit number)

20575312067651098380…94606224981790299839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.057 × 10⁹⁸(99-digit number)

20575312067651098380…94606224981790299841

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 #566,725

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