Block #544,382

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/14/2014, 8:46:56 PM · Difficulty 10.9504 · 6,263,872 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

939398fb8a73bd429853d3ad4d0914d7499e971ae8388e08d3af997d5373e904

View on Chainz ↗

Height

#544,382

Difficulty

10.950438

Transactions

Size

903 B

Version

Bits

0af34ff0

Nonce

667,978,689

Timestamp

5/14/2014, 8:46:56 PM

Confirmations

6,263,872

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a6e800bf9d8fef69dfda439ae6983787f7155abc59bb6683d44e5ba2340aa3d3

Transactions (2)

Coinbase347306c568659c…fe2d84b44d1419

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

407e3803d67cae…84fbce1f791f2f

3 in → 8 out8.7753 XPM695 B

APPZLZRh…k8wT1gVi AUag3UWu…qBS5raDH AQv2iMwd…EFna22ee ASY5xqVU…DNRfWDXj AU8Gx9wF…Dof9VtwY

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.

5.234 × 10⁹⁸(99-digit number)

52340429385876338532…34822954437466217119

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

5.234 × 10⁹⁸(99-digit number)

52340429385876338532…34822954437466217119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.234 × 10⁹⁸(99-digit number)

52340429385876338532…34822954437466217121

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

1.046 × 10⁹⁹(100-digit number)

10468085877175267706…69645908874932434239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.046 × 10⁹⁹(100-digit number)

10468085877175267706…69645908874932434241

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

2.093 × 10⁹⁹(100-digit number)

20936171754350535412…39291817749864868479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.093 × 10⁹⁹(100-digit number)

20936171754350535412…39291817749864868481

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

4.187 × 10⁹⁹(100-digit number)

41872343508701070825…78583635499729736959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.187 × 10⁹⁹(100-digit number)

41872343508701070825…78583635499729736961

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

8.374 × 10⁹⁹(100-digit number)

83744687017402141651…57167270999459473919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.374 × 10⁹⁹(100-digit number)

83744687017402141651…57167270999459473921

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 #544,382

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