Block #254,877

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/10/2013, 11:24:13 PM · Difficulty 9.9736 · 6,571,176 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

176fc0fb354c466d97c67f713d56592141ab024cea332b63900c370a11512488

View on Chainz ↗

Height

#254,877

Difficulty

9.973589

Transactions

Size

896 B

Version

Bits

09f93d23

Nonce

102

Timestamp

11/10/2013, 11:24:13 PM

Confirmations

6,571,176

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

12d9890349e6124e1b8391a2c50b93db52af2645cc7eee7499f907670c628452

Transactions (2)

Coinbaseae9811085860f5…cd93cf269075fd

1 in → 2 out10.0500 XPM136 B

ARmAMwyu…P7Kn74ZT Abiw8n3q…ZnZfgvQW

5d056777262f10…bc01f05d48fa0a

4 in → 2 out28.8151 XPM669 B

AXyFswJU…PASmwgJD ARzvPmNb…rr2vazU5

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.

1.418 × 10⁹⁶(97-digit number)

14185618881624508225…32922581525709887999

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

1.418 × 10⁹⁶(97-digit number)

14185618881624508225…32922581525709887999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.418 × 10⁹⁶(97-digit number)

14185618881624508225…32922581525709888001

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

2.837 × 10⁹⁶(97-digit number)

28371237763249016451…65845163051419775999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.837 × 10⁹⁶(97-digit number)

28371237763249016451…65845163051419776001

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

5.674 × 10⁹⁶(97-digit number)

56742475526498032903…31690326102839551999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.674 × 10⁹⁶(97-digit number)

56742475526498032903…31690326102839552001

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

1.134 × 10⁹⁷(98-digit number)

11348495105299606580…63380652205679103999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.134 × 10⁹⁷(98-digit number)

11348495105299606580…63380652205679104001

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

2.269 × 10⁹⁷(98-digit number)

22696990210599213161…26761304411358207999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.269 × 10⁹⁷(98-digit number)

22696990210599213161…26761304411358208001

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 #254,877

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