Block #253,016

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 9:44:16 PM · Difficulty 9.9718 · 6,557,959 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e929f4ca14e59056cab3b7dcfa6daa0c4687d69cb3957f32cf66d535d475163b

View on Chainz ↗

Height

#253,016

Difficulty

9.971842

Transactions

Size

2.14 KB

Version

Bits

09f8caa4

Nonce

223,880

Timestamp

11/9/2013, 9:44:16 PM

Confirmations

6,557,959

Mined by

⛏️ XaR~AeVd75V5bi5osYWi2nWRDS1d3zcWrWFmHo

Merkle Root

f386a3f77e8a37576875154a11da3a680c928c7a7118f5b4060d6b9799bb9b13

Transactions (1)

Coinbasef386a3f77e8a37…0d6b9799bb9b13

1 in → 60 out10.0100 XPM2.05 KB

AeVd75V5…cWrWFmHo AdnG9gQ7…N9B7mA2p AdL4ZZDR…2eQtg1T9 AQtzUSwq…htAuF3yC AScCYXya…oAz38X3p

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.

1.762 × 10⁸⁸(89-digit number)

17625512158111905103…25114021721231037119

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

1.762 × 10⁸⁸(89-digit number)

17625512158111905103…25114021721231037119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.762 × 10⁸⁸(89-digit number)

17625512158111905103…25114021721231037121

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

3.525 × 10⁸⁸(89-digit number)

35251024316223810206…50228043442462074239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.525 × 10⁸⁸(89-digit number)

35251024316223810206…50228043442462074241

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

7.050 × 10⁸⁸(89-digit number)

70502048632447620412…00456086884924148479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.050 × 10⁸⁸(89-digit number)

70502048632447620412…00456086884924148481

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

1.410 × 10⁸⁹(90-digit number)

14100409726489524082…00912173769848296959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.410 × 10⁸⁹(90-digit number)

14100409726489524082…00912173769848296961

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

2.820 × 10⁸⁹(90-digit number)

28200819452979048164…01824347539696593919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.820 × 10⁸⁹(90-digit number)

28200819452979048164…01824347539696593921

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 #253,016

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