Block #255,203

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/11/2013, 3:39:29 AM · Difficulty 9.9740 · 6,552,404 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

076759c5c57d3704a8aee29cc1494118f4647eeb8d0553872a5745d589c42dcc

View on Chainz ↗

Height

#255,203

Difficulty

9.973969

Transactions

Size

2.17 KB

Version

Bits

09f95604

Nonce

418,604

Timestamp

11/11/2013, 3:39:29 AM

Confirmations

6,552,404

Mined by

⛏️ aRQXvARR7aRH6ng9G4v4WFreBpLwkEdne3DXGXZ

Merkle Root

0449e2d17edc5855a449baa5c4c04a94f68e294292ef4458bed240722664d9af

Transactions (4)

Coinbasedd5b87dc387982…d3aedc27209603

1 in → 41 out10.0200 XPM1.42 KB

ARR7aRH6…ne3DXGXZ AQtzUSwq…htAuF3yC AQQMyJDA…xUZhKMrK APgWZwJ2…1nTrECFn AeNjg8HA…9AkdpcSC

cac717b8787198…e4d2e4938bbdc6

1 in → 2 out10.0300 XPM226 B

AK5WQud3…QmxRG8R8 AKNaPgZg…UFrKNhGe

fa980ddaef5b45…06b7b7b367418e

1 in → 2 out3.1700 XPM226 B

AUgb7pz8…CzVtk6rm ALCKW4FA…T6xHvxka

3a0dd334d2302b…b78b801e3640fe

1 in → 2 out8.0158 XPM226 B

AeuxzbY8…3ocRXaYE AaVFHFSq…bCnX1Bpw

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.

4.020 × 10⁹⁵(96-digit number)

40206691143890032672…92161819924706522879

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

4.020 × 10⁹⁵(96-digit number)

40206691143890032672…92161819924706522879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.020 × 10⁹⁵(96-digit number)

40206691143890032672…92161819924706522881

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

8.041 × 10⁹⁵(96-digit number)

80413382287780065344…84323639849413045759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.041 × 10⁹⁵(96-digit number)

80413382287780065344…84323639849413045761

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

1.608 × 10⁹⁶(97-digit number)

16082676457556013068…68647279698826091519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.608 × 10⁹⁶(97-digit number)

16082676457556013068…68647279698826091521

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

3.216 × 10⁹⁶(97-digit number)

32165352915112026137…37294559397652183039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.216 × 10⁹⁶(97-digit number)

32165352915112026137…37294559397652183041

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

6.433 × 10⁹⁶(97-digit number)

64330705830224052275…74589118795304366079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.433 × 10⁹⁶(97-digit number)

64330705830224052275…74589118795304366081

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 #255,203

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