Block #566,722

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/29/2014, 2:57:16 AM · Difficulty 10.9660 · 6,250,445 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6e43579fadfedc8bf380a46b6eb240ea4c35ab6e4fe473f9ea7c17fc49e33baf

View on Chainz ↗

Height

#566,722

Difficulty

10.966028

Transactions

Size

658 B

Version

Bits

0af74da2

Nonce

32,779,811

Timestamp

5/29/2014, 2:57:16 AM

Confirmations

6,250,445

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1abbb0e16658baddb79d7669bfe6079809351b21060b8e4fe03d2f230c3171b4

Transactions (3)

Coinbase0fcd6e0b5f64a8…30ee29a538b5d8

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

7a7d5a8ae70978…866d28a500228c

1 in → 2 out7.2750 XPM225 B

AcJNvrYj…HyP8mWJd AGFD3Ho1…J57ViRCn

ee2216ea21d284…e31412530e5fbc

1 in → 2 out4.1848 XPM226 B

AcHLVrZR…SU5ENSw1 AWEm1NVx…BSyUpTdF

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.

1.767 × 10⁹⁸(99-digit number)

17672210125136569688…08488929022572531519

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

1.767 × 10⁹⁸(99-digit number)

17672210125136569688…08488929022572531519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.767 × 10⁹⁸(99-digit number)

17672210125136569688…08488929022572531521

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

3.534 × 10⁹⁸(99-digit number)

35344420250273139377…16977858045145063039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.534 × 10⁹⁸(99-digit number)

35344420250273139377…16977858045145063041

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

7.068 × 10⁹⁸(99-digit number)

70688840500546278754…33955716090290126079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.068 × 10⁹⁸(99-digit number)

70688840500546278754…33955716090290126081

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

1.413 × 10⁹⁹(100-digit number)

14137768100109255750…67911432180580252159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.413 × 10⁹⁹(100-digit number)

14137768100109255750…67911432180580252161

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

2.827 × 10⁹⁹(100-digit number)

28275536200218511501…35822864361160504319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.827 × 10⁹⁹(100-digit number)

28275536200218511501…35822864361160504321

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 #566,722

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