Block #438,314

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/10/2014, 9:57:37 PM · Difficulty 10.3600 · 6,356,326 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

df5f2a6f256762b4882e1fee3a1c3b182c0385b827f2d5f78d9b95bb7baaf2cc

View on Chainz ↗

Height

#438,314

Difficulty

10.359989

Transactions

Size

1.70 KB

Version

Bits

0a5c2836

Nonce

1,024,201

Timestamp

3/10/2014, 9:57:37 PM

Confirmations

6,356,326

Mined by

⛏️ P2SHAJyMF5m6bfmy8MZ1Uyozeo5gpH7BzQCCQQ

Merkle Root

8c04a5aa9fa22b94a686594b7fca4fa44319aadb4a262fc1c26d6f3684b868ee

Transactions (4)

Coinbase9d8267e31a35c5…a85f4a0c2ffa4c

1 in → 1 out9.3400 XPM109 B

AJyMF5m6…7BzQCCQQ

3e5f6e2cd08c1d…f8bb33d0d2bfe5

5 in → 14 out43.8323 XPM1.06 KB

ALx3425Y…r8Li6UPm AG2JTScj…ChuVCmLt AdVJEi62…5WZTgbE1 AXz2q38A…TQbL4EfA ALo6jyqD…xLBCAeaV

a719714de32366…844e3c95ba1426

1 in → 2 out8.2078 XPM227 B

AaNiMZ52…NYa3G6ez AVRd7YP6…GtHtjhBS

b154ebba49ad7d…25c6cfadecf21e

1 in → 2 out1.8299 XPM226 B

AbDBuYFj…Ys9qhQsE AcMyqdka…JRxpR786

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.

3.261 × 10⁹⁸(99-digit number)

32615719881402704295…68462637904125850879

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

3.261 × 10⁹⁸(99-digit number)

32615719881402704295…68462637904125850879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.261 × 10⁹⁸(99-digit number)

32615719881402704295…68462637904125850881

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

6.523 × 10⁹⁸(99-digit number)

65231439762805408590…36925275808251701759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.523 × 10⁹⁸(99-digit number)

65231439762805408590…36925275808251701761

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

1.304 × 10⁹⁹(100-digit number)

13046287952561081718…73850551616503403519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.304 × 10⁹⁹(100-digit number)

13046287952561081718…73850551616503403521

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

2.609 × 10⁹⁹(100-digit number)

26092575905122163436…47701103233006807039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.609 × 10⁹⁹(100-digit number)

26092575905122163436…47701103233006807041

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

5.218 × 10⁹⁹(100-digit number)

52185151810244326872…95402206466013614079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.218 × 10⁹⁹(100-digit number)

52185151810244326872…95402206466013614081

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