Block #431,232

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/6/2014, 2:07:54 AM · Difficulty 10.3384 · 6,364,201 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

97274fdd1b68b7ab1658f68f03ea3317b2e1ecf400499079b8ffa1ad7a40f50d

View on Chainz ↗

Height

#431,232

Difficulty

10.338399

Transactions

Size

1.93 KB

Version

Bits

0a56a14a

Nonce

1,168

Timestamp

3/6/2014, 2:07:54 AM

Confirmations

6,364,201

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

fcd7c5e1686c7bbc6142feb71f78ea44e5d86c1d5823980e2cf69d60fb3dbd6a

Transactions (3)

Coinbasee82e047b2f7266…a355b18677ef99

1 in → 1 out9.3700 XPM116 B

AbwWkWZt…kawDhufa

67a5d3edea00ac…165112052e53d8

4 in → 2 out12.8840 XPM672 B

AQLnNJJ7…h1WxPboq AMHwyiui…TNUqyCKG

f9ac9bbd4aa7ea…0b874b6319b508

5 in → 15 out46.6300 XPM1.07 KB

AaSPQSre…sBC9fTQR ARNnMS5i…KVgiuUaq AZr7Wijk…hp5mw6Tj AL5wNHbW…dFU2npvz AXWdmUfv…DmgM1U8i

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.

1.135 × 10¹⁰²(103-digit number)

11357848667943885591…16519790642428641279

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

1.135 × 10¹⁰²(103-digit number)

11357848667943885591…16519790642428641279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.135 × 10¹⁰²(103-digit number)

11357848667943885591…16519790642428641281

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

2.271 × 10¹⁰²(103-digit number)

22715697335887771182…33039581284857282559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.271 × 10¹⁰²(103-digit number)

22715697335887771182…33039581284857282561

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

4.543 × 10¹⁰²(103-digit number)

45431394671775542364…66079162569714565119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.543 × 10¹⁰²(103-digit number)

45431394671775542364…66079162569714565121

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

9.086 × 10¹⁰²(103-digit number)

90862789343551084729…32158325139429130239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.086 × 10¹⁰²(103-digit number)

90862789343551084729…32158325139429130241

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

1.817 × 10¹⁰³(104-digit number)

18172557868710216945…64316650278858260479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.817 × 10¹⁰³(104-digit number)

18172557868710216945…64316650278858260481

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