Block #275,286

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 3:36:52 PM · Difficulty 9.9603 · 6,535,308 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b5db2a57f26463c6e3cad318c68304b4c3677f601805eda0dfe723b85dbf8525

View on Chainz ↗

Height

#275,286

Difficulty

9.960296

Transactions

Size

719 B

Version

Bits

09f5d5f3

Nonce

22,386

Timestamp

11/26/2013, 3:36:52 PM

Confirmations

6,535,308

Mined by

⛏️ P2SHAZgYtNSG5AreNkuRBWQhbqCMyJdpr1Hcz2

Merkle Root

d267d533972498d0a3fd325e43368e9e838c3e00c96c91b3ebc50005c5622383

Transactions (2)

Coinbase4bc9a3d9f428c2…70c593a6cc93e5

1 in → 1 out10.0700 XPM109 B

AZgYtNSG…dpr1Hcz2

c7bdfc20a08ae1…ffb4ecc61296f4

3 in → 2 out2.9948 XPM521 B

ANjPTYiM…Quya7q5k APaz452Y…pze4QrBe

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.

1.478 × 10⁹¹(92-digit number)

14788537542005829418…24049018507973238119

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

1.478 × 10⁹¹(92-digit number)

14788537542005829418…24049018507973238119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.478 × 10⁹¹(92-digit number)

14788537542005829418…24049018507973238121

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

2.957 × 10⁹¹(92-digit number)

29577075084011658836…48098037015946476239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.957 × 10⁹¹(92-digit number)

29577075084011658836…48098037015946476241

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

5.915 × 10⁹¹(92-digit number)

59154150168023317672…96196074031892952479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.915 × 10⁹¹(92-digit number)

59154150168023317672…96196074031892952481

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

1.183 × 10⁹²(93-digit number)

11830830033604663534…92392148063785904959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.183 × 10⁹²(93-digit number)

11830830033604663534…92392148063785904961

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

2.366 × 10⁹²(93-digit number)

23661660067209327068…84784296127571809919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.366 × 10⁹²(93-digit number)

23661660067209327068…84784296127571809921

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 #275,286

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