Block #335,569

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/30/2013, 8:28:34 AM · Difficulty 10.1455 · 6,472,418 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8852ceb0ccaaeee46f3feacdf43ae1aca8392c0c53c0acc269c0d7a409d8c0c2

View on Chainz ↗

Height

#335,569

Difficulty

10.145500

Transactions

Size

1.01 KB

Version

Bits

0a253f82

Nonce

603,664

Timestamp

12/30/2013, 8:28:34 AM

Confirmations

6,472,418

Mined by

⛏️ aR.$APsPtagSLffEQxQzpfFFBusZHkismQazQb

Merkle Root

8c2e2ae0b9394e0c5f59353f7fffbeb08621c993266e2954e48b24e1dcfb25a0

Transactions (1)

Coinbase8c2e2ae0b9394e…8b24e1dcfb25a0

1 in → 26 out9.7000 XPM947 B

APsPtagS…ismQazQb AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1 Aac9Hjdg…P4ktypc3 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.

4.023 × 10⁹⁸(99-digit number)

40236762379113420170…57223429111499979039

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

4.023 × 10⁹⁸(99-digit number)

40236762379113420170…57223429111499979039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.023 × 10⁹⁸(99-digit number)

40236762379113420170…57223429111499979041

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

8.047 × 10⁹⁸(99-digit number)

80473524758226840341…14446858222999958079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.047 × 10⁹⁸(99-digit number)

80473524758226840341…14446858222999958081

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

1.609 × 10⁹⁹(100-digit number)

16094704951645368068…28893716445999916159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.609 × 10⁹⁹(100-digit number)

16094704951645368068…28893716445999916161

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

3.218 × 10⁹⁹(100-digit number)

32189409903290736136…57787432891999832319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.218 × 10⁹⁹(100-digit number)

32189409903290736136…57787432891999832321

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

6.437 × 10⁹⁹(100-digit number)

64378819806581472273…15574865783999664639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.437 × 10⁹⁹(100-digit number)

64378819806581472273…15574865783999664641

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 #335,569

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