Block #472,436

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/3/2014, 7:04:58 AM · Difficulty 10.4336 · 6,335,288 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6e26f233404940dbe058612a41ae1617199fad5b029a3544617bb4b39f8b7cac

View on Chainz ↗

Height

#472,436

Difficulty

10.433597

Transactions

Size

620 B

Version

Bits

0a6f003c

Nonce

9,799

Timestamp

4/3/2014, 7:04:58 AM

Confirmations

6,335,288

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

05cbaaf0f84c2485b7eea9c53cb6073b6f22adb5d13133404f59ee3150c8497d

Transactions (3)

Coinbaseac48574cd08658…fc5eeba0ed7b22

1 in → 1 out9.1900 XPM110 B

AeKNrjNj…1NEq95Ta

2b6e16366a7d70…0d5890b2a8f529

1 in → 3 out9.2000 XPM226 B

AeKNrjNj…1NEq95Ta AWjbJ2on…vc84xGe1 AHXJ1dhk…mhL46N6m

c1852219760733…b9ecc902899713

1 in → 1 out2.9903 XPM193 B

ASLwqNEo…1ccEZYHV

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.

2.252 × 10⁹⁶(97-digit number)

22528082061803892238…63179574673601177599

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

2.252 × 10⁹⁶(97-digit number)

22528082061803892238…63179574673601177599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.252 × 10⁹⁶(97-digit number)

22528082061803892238…63179574673601177601

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

4.505 × 10⁹⁶(97-digit number)

45056164123607784476…26359149347202355199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.505 × 10⁹⁶(97-digit number)

45056164123607784476…26359149347202355201

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

9.011 × 10⁹⁶(97-digit number)

90112328247215568953…52718298694404710399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.011 × 10⁹⁶(97-digit number)

90112328247215568953…52718298694404710401

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

1.802 × 10⁹⁷(98-digit number)

18022465649443113790…05436597388809420799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.802 × 10⁹⁷(98-digit number)

18022465649443113790…05436597388809420801

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

3.604 × 10⁹⁷(98-digit number)

36044931298886227581…10873194777618841599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.604 × 10⁹⁷(98-digit number)

36044931298886227581…10873194777618841601

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 #472,436

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