Block #568,666

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/30/2014, 3:03:05 PM · Difficulty 10.9646 · 6,242,325 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

18034eddc003994ad9f0e1e7229ca82afe7d9dfba91b0feb8d3367d44e648024

View on Chainz ↗

Height

#568,666

Difficulty

10.964583

Transactions

Size

806 B

Version

Bits

0af6eeec

Nonce

792,729,349

Timestamp

5/30/2014, 3:03:05 PM

Confirmations

6,242,325

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

76fa57c2e8548a9e5a2790cc92ac718898b468ea273cef894cae523897c5c601

Transactions (3)

Coinbasefd2553988993a3…8b24e94844a85b

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

a1a8a369d33228…4b5cedf91fd0f3

2 in → 2 out449.0100 XPM373 B

APCXtBZF…o6PW8U1R AHpTVnM2…PopTdZeF

e6c33b65ef5d28…96c9793ee1c0b9

1 in → 2 out4.1187 XPM226 B

AJPMAkhf…WnZtjDqR AGdWVjRk…LFVsqCnK

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.

1.015 × 10⁹⁸(99-digit number)

10158006778263850339…82861685780572468479

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

1.015 × 10⁹⁸(99-digit number)

10158006778263850339…82861685780572468479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.015 × 10⁹⁸(99-digit number)

10158006778263850339…82861685780572468481

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

2.031 × 10⁹⁸(99-digit number)

20316013556527700678…65723371561144936959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.031 × 10⁹⁸(99-digit number)

20316013556527700678…65723371561144936961

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

4.063 × 10⁹⁸(99-digit number)

40632027113055401357…31446743122289873919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.063 × 10⁹⁸(99-digit number)

40632027113055401357…31446743122289873921

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

8.126 × 10⁹⁸(99-digit number)

81264054226110802714…62893486244579747839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.126 × 10⁹⁸(99-digit number)

81264054226110802714…62893486244579747841

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

1.625 × 10⁹⁹(100-digit number)

16252810845222160542…25786972489159495679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.625 × 10⁹⁹(100-digit number)

16252810845222160542…25786972489159495681

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 #568,666

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