Block #405,754

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/15/2014, 6:53:20 PM · Difficulty 10.4326 · 6,400,296 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c56c77a5abd695ba9f5e46197e075265db7adcdaec29efb7d7f2608b3e7c5519

View on Chainz ↗

Height

#405,754

Difficulty

10.432573

Transactions

Size

833 B

Version

Bits

0a6ebd21

Nonce

18,082

Timestamp

2/15/2014, 6:53:20 PM

Confirmations

6,400,296

Mined by

⛏️ 0aRkAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

7bbd49b4381b4d111076d3f2ca6a1682514510a71483f16866f94e1553c51055

Transactions (1)

Coinbase7bbd49b4381b4d…f94e1553c51055

1 in → 20 out9.1700 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AH8yR9wQ…3GmoUBGQ

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.

3.454 × 10⁹⁵(96-digit number)

34544577584663543532…67798885327942995199

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

3.454 × 10⁹⁵(96-digit number)

34544577584663543532…67798885327942995199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.454 × 10⁹⁵(96-digit number)

34544577584663543532…67798885327942995201

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

6.908 × 10⁹⁵(96-digit number)

69089155169327087065…35597770655885990399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.908 × 10⁹⁵(96-digit number)

69089155169327087065…35597770655885990401

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

1.381 × 10⁹⁶(97-digit number)

13817831033865417413…71195541311771980799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.381 × 10⁹⁶(97-digit number)

13817831033865417413…71195541311771980801

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

2.763 × 10⁹⁶(97-digit number)

27635662067730834826…42391082623543961599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.763 × 10⁹⁶(97-digit number)

27635662067730834826…42391082623543961601

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

5.527 × 10⁹⁶(97-digit number)

55271324135461669652…84782165247087923199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.527 × 10⁹⁶(97-digit number)

55271324135461669652…84782165247087923201

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