Block #392,522

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/6/2014, 12:38:25 PM · Difficulty 10.4389 · 6,411,682 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6a3961cee422215060425f8d8082b5e1f06ceb048477bd2aabfe60221c91bdf4

View on Chainz ↗

Height

#392,522

Difficulty

10.438920

Transactions

Size

834 B

Version

Bits

0a705d12

Nonce

23,170

Timestamp

2/6/2014, 12:38:25 PM

Confirmations

6,411,682

Mined by

⛏️ JaR!AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

69efea5517ea16d657dd80f8d55eaae808f932bd3c7b2a1c273742562003d5ef

Transactions (1)

Coinbase69efea5517ea16…3742562003d5ef

1 in → 20 out9.1600 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AZV4TwxQ…8JnQqSoH

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.

1.127 × 10⁹⁶(97-digit number)

11278909204264192057…96472108888859179999

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

1.127 × 10⁹⁶(97-digit number)

11278909204264192057…96472108888859179999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.127 × 10⁹⁶(97-digit number)

11278909204264192057…96472108888859180001

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

2.255 × 10⁹⁶(97-digit number)

22557818408528384115…92944217777718359999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.255 × 10⁹⁶(97-digit number)

22557818408528384115…92944217777718360001

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

4.511 × 10⁹⁶(97-digit number)

45115636817056768230…85888435555436719999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.511 × 10⁹⁶(97-digit number)

45115636817056768230…85888435555436720001

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

9.023 × 10⁹⁶(97-digit number)

90231273634113536461…71776871110873439999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.023 × 10⁹⁶(97-digit number)

90231273634113536461…71776871110873440001

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

1.804 × 10⁹⁷(98-digit number)

18046254726822707292…43553742221746879999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.804 × 10⁹⁷(98-digit number)

18046254726822707292…43553742221746880001

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