Block #403,332

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/14/2014, 2:31:28 AM · Difficulty 10.4312 · 6,406,236 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4d5526d1f98044bb62f7dd2b24d839fe98660965ef898d638e6c19babc6eae16

View on Chainz ↗

Height

#403,332

Difficulty

10.431231

Transactions

Size

595 B

Version

Bits

0a6e652e

Nonce

137,856

Timestamp

2/14/2014, 2:31:28 AM

Confirmations

6,406,236

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

45c768ae8d18167a69b1287ab977355d5b2b60f5406223b59dc872d8be985dc1

Transactions (3)

Coinbase8c76f5054b35ce…67c9314ee58706

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

81853751224401…ae79671826ca86

1 in → 2 out80.2796 XPM226 B

AM3Jf7aB…3vZdFrkq AaWb8zLQ…jQaftzao

a01aadc1a5d38c…10a7f319c529c5

1 in → 1 out9.2000 XPM157 B

AbP1iY2S…QXTtEVYb

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.

2.164 × 10¹⁰⁸(109-digit number)

21649203428552672782…91321222204374879919

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

2.164 × 10¹⁰⁸(109-digit number)

21649203428552672782…91321222204374879919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.164 × 10¹⁰⁸(109-digit number)

21649203428552672782…91321222204374879921

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

4.329 × 10¹⁰⁸(109-digit number)

43298406857105345565…82642444408749759839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.329 × 10¹⁰⁸(109-digit number)

43298406857105345565…82642444408749759841

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

8.659 × 10¹⁰⁸(109-digit number)

86596813714210691131…65284888817499519679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.659 × 10¹⁰⁸(109-digit number)

86596813714210691131…65284888817499519681

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

1.731 × 10¹⁰⁹(110-digit number)

17319362742842138226…30569777634999039359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.731 × 10¹⁰⁹(110-digit number)

17319362742842138226…30569777634999039361

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

3.463 × 10¹⁰⁹(110-digit number)

34638725485684276452…61139555269998078719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.463 × 10¹⁰⁹(110-digit number)

34638725485684276452…61139555269998078721

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 #403,332

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