Block #404,729

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/15/2014, 1:31:51 AM · Difficulty 10.4335 · 6,405,927 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c7bf5b252388e573a7fd01702f1cd235ba2684da9cd63a93f45cd8ef1bd51177

View on Chainz ↗

Height

#404,729

Difficulty

10.433507

Transactions

Size

969 B

Version

Bits

0a6efa4d

Nonce

42,284

Timestamp

2/15/2014, 1:31:51 AM

Confirmations

6,405,927

Mined by

⛏️ ,aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

9f1eb60de9b3291556f779c5853a1c79665bb1d673d9ebceb0797ab3f5839f3b

Transactions (1)

Coinbase9f1eb60de9b329…797ab3f5839f3b

1 in → 24 out9.1700 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ATKK7iFz…wZm46KN1 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.

6.982 × 10⁹⁴(95-digit number)

69822650067797859508…65728803043764802809

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

6.982 × 10⁹⁴(95-digit number)

69822650067797859508…65728803043764802809

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.982 × 10⁹⁴(95-digit number)

69822650067797859508…65728803043764802811

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

1.396 × 10⁹⁵(96-digit number)

13964530013559571901…31457606087529605619

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.396 × 10⁹⁵(96-digit number)

13964530013559571901…31457606087529605621

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

2.792 × 10⁹⁵(96-digit number)

27929060027119143803…62915212175059211239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.792 × 10⁹⁵(96-digit number)

27929060027119143803…62915212175059211241

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

5.585 × 10⁹⁵(96-digit number)

55858120054238287606…25830424350118422479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.585 × 10⁹⁵(96-digit number)

55858120054238287606…25830424350118422481

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

1.117 × 10⁹⁶(97-digit number)

11171624010847657521…51660848700236844959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.117 × 10⁹⁶(97-digit number)

11171624010847657521…51660848700236844961

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 #404,729

Cookie Preferences