Block #392,296

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/6/2014, 9:11:01 AM · Difficulty 10.4369 · 6,403,802 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

712d4d023f48c9ea95d64377e25c5c7bb5324b5da22921484719afdc0b6a87ce

View on Chainz ↗

Height

#392,296

Difficulty

10.436916

Transactions

Size

899 B

Version

Bits

0a6fd9b5

Nonce

194,476

Timestamp

2/6/2014, 9:11:01 AM

Confirmations

6,403,802

Mined by

⛏️ haRQAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

b67ddc512acf30ec5141f03246d65ff053c10b8c0d4b90dac61a58eefb7fbd36

Transactions (1)

Coinbaseb67ddc512acf30…1a58eefb7fbd36

1 in → 22 out9.1700 XPM810 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.

1.269 × 10⁹¹(92-digit number)

12696396944507153963…37117826778738899999

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

1.269 × 10⁹¹(92-digit number)

12696396944507153963…37117826778738899999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.269 × 10⁹¹(92-digit number)

12696396944507153963…37117826778738900001

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

2.539 × 10⁹¹(92-digit number)

25392793889014307926…74235653557477799999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.539 × 10⁹¹(92-digit number)

25392793889014307926…74235653557477800001

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

5.078 × 10⁹¹(92-digit number)

50785587778028615853…48471307114955599999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.078 × 10⁹¹(92-digit number)

50785587778028615853…48471307114955600001

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

1.015 × 10⁹²(93-digit number)

10157117555605723170…96942614229911199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.015 × 10⁹²(93-digit number)

10157117555605723170…96942614229911200001

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

2.031 × 10⁹²(93-digit number)

20314235111211446341…93885228459822399999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.031 × 10⁹²(93-digit number)

20314235111211446341…93885228459822400001

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