Block #336,423

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/30/2013, 10:54:08 PM · Difficulty 10.1431 · 6,489,079 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e3c3c8d12d725c0ecf210a6340d4bb8345ccd087071d791c2bda0961b477ddab

View on Chainz ↗

Height

#336,423

Difficulty

10.143082

Transactions

Size

1005 B

Version

Bits

0a24a10e

Nonce

345,480

Timestamp

12/30/2013, 10:54:08 PM

Confirmations

6,489,079

Mined by

⛏️ '"aR_kAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

9ffd8970633b0bd68b8d4adcb21f49d1eeb4f2981428c0082ca3455797c4523c

Transactions (1)

Coinbase9ffd8970633b0b…a3455797c4523c

1 in → 25 out9.7100 XPM913 B

AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz

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.

2.258 × 10⁹⁹(100-digit number)

22580731634752399524…78755692383221575679

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

2.258 × 10⁹⁹(100-digit number)

22580731634752399524…78755692383221575679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.258 × 10⁹⁹(100-digit number)

22580731634752399524…78755692383221575681

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

4.516 × 10⁹⁹(100-digit number)

45161463269504799049…57511384766443151359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.516 × 10⁹⁹(100-digit number)

45161463269504799049…57511384766443151361

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

9.032 × 10⁹⁹(100-digit number)

90322926539009598098…15022769532886302719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.032 × 10⁹⁹(100-digit number)

90322926539009598098…15022769532886302721

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

1.806 × 10¹⁰⁰(101-digit number)

18064585307801919619…30045539065772605439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.806 × 10¹⁰⁰(101-digit number)

18064585307801919619…30045539065772605441

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

3.612 × 10¹⁰⁰(101-digit number)

36129170615603839239…60091078131545210879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.612 × 10¹⁰⁰(101-digit number)

36129170615603839239…60091078131545210881

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 #336,423

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