Block #262,916

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/17/2013, 8:01:27 AM · Difficulty 9.9674 · 6,579,112 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

743ac256ddc2e78060a9040a7660b88cb4a9a9e22eb3b2312f904c00984a9aad

View on Chainz ↗

Height

#262,916

Difficulty

9.967370

Transactions

Size

2.40 KB

Version

Bits

09f7a593

Nonce

10,091

Timestamp

11/17/2013, 8:01:27 AM

Confirmations

6,579,112

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

0f44d5e40aa6daad3c6f125ca79dc17f9cd0c9ad3e6dff13b1f00abed8dc6b79

Transactions (5)

Coinbase53154bd4d27c6b…77e6b042b2bff4

1 in → 2 out10.1000 XPM136 B

AKcbk49N…GJbKa7j1 ALfEGCwh…VawujfMm

36621fd36cd4e6…5f3d91f91529cb

1 in → 2 out10.0300 XPM193 B

AJLvthAi…3TBnjh6B AKjmNhNv…VmRh3Hz4

aeaca370029856…10c54385d396e5

2 in → 3 out4.4067 XPM407 B

AHxYYRbr…GGanm5Eo AbfCgbJo…nKh3oLTK AeKMWcDE…P2CJFDrL

f7d0dbd5b4da48…99d5b3ad330e48

2 in → 2 out2.2000 XPM373 B

AQiXSyhz…3eDkP7Ls AQSr5BKX…Dni6XyUH

30f83526e884c3…e81a083b12b862

8 in → 2 out2.6544 XPM1.23 KB

AQiXSyhz…3eDkP7Ls ASGtn54h…sQYYHQ31

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.

6.879 × 10⁹⁶(97-digit number)

68791859559686320612…11508702840904158719

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

6.879 × 10⁹⁶(97-digit number)

68791859559686320612…11508702840904158719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.879 × 10⁹⁶(97-digit number)

68791859559686320612…11508702840904158721

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

1.375 × 10⁹⁷(98-digit number)

13758371911937264122…23017405681808317439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.375 × 10⁹⁷(98-digit number)

13758371911937264122…23017405681808317441

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

2.751 × 10⁹⁷(98-digit number)

27516743823874528245…46034811363616634879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.751 × 10⁹⁷(98-digit number)

27516743823874528245…46034811363616634881

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

5.503 × 10⁹⁷(98-digit number)

55033487647749056490…92069622727233269759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.503 × 10⁹⁷(98-digit number)

55033487647749056490…92069622727233269761

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

1.100 × 10⁹⁸(99-digit number)

11006697529549811298…84139245454466539519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.100 × 10⁹⁸(99-digit number)

11006697529549811298…84139245454466539521

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 #262,916

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