Block #283,260

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 4:23:58 PM · Difficulty 9.9808 · 6,527,563 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ea7bff7afdaf5d19023746ba6c37b6ae81644aa3a4736b1464b553b6f9df343d

View on Chainz ↗

Height

#283,260

Difficulty

9.980770

Transactions

Size

426 B

Version

Bits

09fb13be

Nonce

6,225

Timestamp

11/29/2013, 4:23:58 PM

Confirmations

6,527,563

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

83345308e7c324bad4dd1042a1b9b5fb94fa037575cde08dbb8a397d05e685c6

Transactions (2)

Coinbasebd4e2706d8b41b…b25ebb42948337

1 in → 1 out10.0300 XPM110 B

AeKNrjNj…1NEq95Ta

1f41b494e9dd9b…9cb935ae9f4dae

1 in → 2 out67.3900 XPM227 B

AREaYyFH…BMLN62DF AGeoY9Km…M2f5eoeY

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.

2.470 × 10⁹¹(92-digit number)

24709582929750907454…26667606915686862199

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

2.470 × 10⁹¹(92-digit number)

24709582929750907454…26667606915686862199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.470 × 10⁹¹(92-digit number)

24709582929750907454…26667606915686862201

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

4.941 × 10⁹¹(92-digit number)

49419165859501814908…53335213831373724399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.941 × 10⁹¹(92-digit number)

49419165859501814908…53335213831373724401

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

9.883 × 10⁹¹(92-digit number)

98838331719003629816…06670427662747448799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.883 × 10⁹¹(92-digit number)

98838331719003629816…06670427662747448801

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

1.976 × 10⁹²(93-digit number)

19767666343800725963…13340855325494897599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.976 × 10⁹²(93-digit number)

19767666343800725963…13340855325494897601

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

3.953 × 10⁹²(93-digit number)

39535332687601451926…26681710650989795199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.953 × 10⁹²(93-digit number)

39535332687601451926…26681710650989795201

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 #283,260

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