Block #392,284

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/6/2014, 9:00:24 AM · Difficulty 10.4370 · 6,415,569 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

679b6302be9c805dbcfee5c63b84428742203d0ff1b883eb8dd33f4c6c4b342a

View on Chainz ↗

Height

#392,284

Difficulty

10.437018

Transactions

Size

834 B

Version

Bits

0a6fe062

Nonce

189,883

Timestamp

2/6/2014, 9:00:24 AM

Confirmations

6,415,569

Mined by

⛏️ \aRNrAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

f1c2d4c33a15699e9aa7a9f9770f2dc581519e29bfc0e3c2a9fb0ed2958a67fb

Transactions (1)

Coinbasef1c2d4c33a1569…fb0ed2958a67fb

1 in → 20 out9.1700 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ATKK7iFz…wZm46KN1 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

3.344 × 10⁹⁷(98-digit number)

33444793908854431687…23161185430305474559

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

3.344 × 10⁹⁷(98-digit number)

33444793908854431687…23161185430305474559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.344 × 10⁹⁷(98-digit number)

33444793908854431687…23161185430305474561

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

6.688 × 10⁹⁷(98-digit number)

66889587817708863374…46322370860610949119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.688 × 10⁹⁷(98-digit number)

66889587817708863374…46322370860610949121

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

1.337 × 10⁹⁸(99-digit number)

13377917563541772674…92644741721221898239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.337 × 10⁹⁸(99-digit number)

13377917563541772674…92644741721221898241

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

2.675 × 10⁹⁸(99-digit number)

26755835127083545349…85289483442443796479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.675 × 10⁹⁸(99-digit number)

26755835127083545349…85289483442443796481

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

5.351 × 10⁹⁸(99-digit number)

53511670254167090699…70578966884887592959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.351 × 10⁹⁸(99-digit number)

53511670254167090699…70578966884887592961

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 #392,284

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