Block #283,474

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/29/2013, 6:06:53 PM · Difficulty 9.9812 · 6,523,712 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dad8c4edc1e2c229e4081d4353fe10ff476998c52bd79279afda7fdc5cb16100

View on Chainz ↗

Height

#283,474

Difficulty

9.981197

Transactions

Size

1.08 KB

Version

Bits

09fb2fb2

Nonce

109,214

Timestamp

11/29/2013, 6:06:53 PM

Confirmations

6,523,712

Mined by

⛏️ RSaRAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

38fe51646a9dda8807415dae4ba4d9fdc1ab98c79fa7f813e7536ec1d998b866

Transactions (1)

Coinbase38fe51646a9dda…536ec1d998b866

1 in → 28 out10.0000 XPM1015 B

AQwRN8bE…V8PsTcY9 AbtgNzNb…9Atvu81w AZ2pPuKg…95SN2Yr7 ALw8WzMm…sj2uYfgL AVss9H5F…zXhyMijY

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.

2.416 × 10⁹³(94-digit number)

24161600638487961717…67057142296967664639

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

2.416 × 10⁹³(94-digit number)

24161600638487961717…67057142296967664639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.416 × 10⁹³(94-digit number)

24161600638487961717…67057142296967664641

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

4.832 × 10⁹³(94-digit number)

48323201276975923434…34114284593935329279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.832 × 10⁹³(94-digit number)

48323201276975923434…34114284593935329281

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

9.664 × 10⁹³(94-digit number)

96646402553951846869…68228569187870658559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.664 × 10⁹³(94-digit number)

96646402553951846869…68228569187870658561

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

1.932 × 10⁹⁴(95-digit number)

19329280510790369373…36457138375741317119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.932 × 10⁹⁴(95-digit number)

19329280510790369373…36457138375741317121

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

3.865 × 10⁹⁴(95-digit number)

38658561021580738747…72914276751482634239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.865 × 10⁹⁴(95-digit number)

38658561021580738747…72914276751482634241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

7.731 × 10⁹⁴(95-digit number)

77317122043161477495…45828553502965268479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #283,474

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