Block #431,168

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/6/2014, 12:34:56 AM · Difficulty 10.3426 · 6,368,362 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a379498e00303a2749ff08a0003bf4ee42d142843affe0b8d05d0c197b6fbc2f

View on Chainz ↗

Height

#431,168

Difficulty

10.342611

Transactions

Size

808 B

Version

Bits

0a57b560

Nonce

4,342

Timestamp

3/6/2014, 12:34:56 AM

Confirmations

6,368,362

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

e4c7bccc2cf7267f5ee83002b3e9b2032159f16a077427bd37e683b5c7e9f21c

Transactions (3)

Coinbased436eaf8117aa6…023c6f264d51b4

1 in → 1 out9.3500 XPM116 B

AbwWkWZt…kawDhufa

bf75e35bd18265…286c7b8be433a2

1 in → 2 out2.0363 XPM226 B

AWf9KZKp…535ZedyP AcPkg4SN…x7yetTt7

0526523e237f4b…b2001741c27a03

2 in → 2 out1.2865 XPM374 B

ANYZgfHj…845CeVgA AYFxzicp…jeAdgy2P

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.

2.585 × 10⁹⁹(100-digit number)

25856045843225613742…21857816244328568479

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

2.585 × 10⁹⁹(100-digit number)

25856045843225613742…21857816244328568479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.585 × 10⁹⁹(100-digit number)

25856045843225613742…21857816244328568481

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

5.171 × 10⁹⁹(100-digit number)

51712091686451227484…43715632488657136959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.171 × 10⁹⁹(100-digit number)

51712091686451227484…43715632488657136961

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

1.034 × 10¹⁰⁰(101-digit number)

10342418337290245496…87431264977314273919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.034 × 10¹⁰⁰(101-digit number)

10342418337290245496…87431264977314273921

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

2.068 × 10¹⁰⁰(101-digit number)

20684836674580490993…74862529954628547839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.068 × 10¹⁰⁰(101-digit number)

20684836674580490993…74862529954628547841

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

4.136 × 10¹⁰⁰(101-digit number)

41369673349160981987…49725059909257095679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.136 × 10¹⁰⁰(101-digit number)

41369673349160981987…49725059909257095681

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