Block #368,746

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/20/2014, 10:21:47 PM · Difficulty 10.4453 · 6,432,263 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

feedab904b2882213010475adfece4e848cf3ccc0a3348ed5adc6976634f8000

View on Chainz ↗

Height

#368,746

Difficulty

10.445311

Transactions

Size

1004 B

Version

Bits

0a71ffe3

Nonce

255,024

Timestamp

1/20/2014, 10:21:47 PM

Confirmations

6,432,263

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

8eccf5a900284c255b8bf53398b4a045011bc2b0b8a47c4ef466fbc513d05b03

Transactions (3)

Coinbaseba90f47c032401…68e52467b7d67a

1 in → 1 out9.1700 XPM116 B

AbwWkWZt…kawDhufa

498f186d545dc4…85c3528f0ec8bd

3 in → 1 out9.0155 XPM490 B

AR7BhNeX…2bRzzJtg

d97cd481c767ef…a2a4c3991e1ff6

2 in → 1 out12.1906 XPM307 B

ALe2nmMK…1cMzemim

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.

1.440 × 10⁹⁸(99-digit number)

14403817301874278625…18680161135107580479

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

1.440 × 10⁹⁸(99-digit number)

14403817301874278625…18680161135107580479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.440 × 10⁹⁸(99-digit number)

14403817301874278625…18680161135107580481

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

2.880 × 10⁹⁸(99-digit number)

28807634603748557251…37360322270215160959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.880 × 10⁹⁸(99-digit number)

28807634603748557251…37360322270215160961

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

5.761 × 10⁹⁸(99-digit number)

57615269207497114503…74720644540430321919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.761 × 10⁹⁸(99-digit number)

57615269207497114503…74720644540430321921

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

1.152 × 10⁹⁹(100-digit number)

11523053841499422900…49441289080860643839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.152 × 10⁹⁹(100-digit number)

11523053841499422900…49441289080860643841

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

2.304 × 10⁹⁹(100-digit number)

23046107682998845801…98882578161721287679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.304 × 10⁹⁹(100-digit number)

23046107682998845801…98882578161721287681

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