Block #406,744

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/16/2014, 11:28:24 AM · Difficulty 10.4322 · 6,418,286 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a73026007c501ef6e724d693c89c7cdeb55eb314afcfd89cbfc99966e79e8266

View on Chainz ↗

Height

#406,744

Difficulty

10.432249

Transactions

Size

1.65 KB

Version

Bits

0a6ea7e7

Nonce

58,022

Timestamp

2/16/2014, 11:28:24 AM

Confirmations

6,418,286

Mined by

⛏️ P2SHAYEzJq7kUZYtKDXvpghi5q28zx7DzDky4R

Merkle Root

7c6633d70a9ab4151b57ac40e7c4041bf3b73c18ade00ec3779f257ced62fd48

Transactions (3)

Coinbase70dc4c43c97d1c…b41b407f5708b7

1 in → 1 out9.1900 XPM109 B

AYEzJq7k…7DzDky4R

b6bf65f50612de…9c02b14db7574a

3 in → 2 out1.8214 XPM522 B

AaSDvHoH…ETYL1CkN aWJVHEq1…UDmybe4Y

9e5a6c2d518b45…c1aa7371e24fa8

6 in → 2 out9.7170 XPM965 B

Aeu6drrW…3VQxfGUt ANDdW4Q4…R8vuwSJR

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.

1.414 × 10⁹⁸(99-digit number)

14142784818887448102…39903442050341904319

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

1.414 × 10⁹⁸(99-digit number)

14142784818887448102…39903442050341904319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.414 × 10⁹⁸(99-digit number)

14142784818887448102…39903442050341904321

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

2.828 × 10⁹⁸(99-digit number)

28285569637774896205…79806884100683808639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.828 × 10⁹⁸(99-digit number)

28285569637774896205…79806884100683808641

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

5.657 × 10⁹⁸(99-digit number)

56571139275549792411…59613768201367617279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.657 × 10⁹⁸(99-digit number)

56571139275549792411…59613768201367617281

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

1.131 × 10⁹⁹(100-digit number)

11314227855109958482…19227536402735234559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.131 × 10⁹⁹(100-digit number)

11314227855109958482…19227536402735234561

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

2.262 × 10⁹⁹(100-digit number)

22628455710219916964…38455072805470469119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.262 × 10⁹⁹(100-digit number)

22628455710219916964…38455072805470469121

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 #406,744

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