Block #410,070

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/18/2014, 7:25:04 PM · Difficulty 10.4302 · 6,386,490 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f344752f0c0981c5ff1af9db3065ba6bb50b164d6bb14264975071ab9e3e6b18

View on Chainz ↗

Height

#410,070

Difficulty

10.430240

Transactions

Size

1.47 KB

Version

Bits

0a6e2435

Nonce

18,912

Timestamp

2/18/2014, 7:25:04 PM

Confirmations

6,386,490

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

e5d541336303008e9d74bfeac1673e7436b4872457ffd95c45c7037a1e072ca5

Transactions (5)

Coinbase8cc1f628245d74…4361c81cff1f5e

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

5db54247e4e939…b831fd5308f63b

3 in → 7 out19.4361 XPM621 B

AVrtTz85…Az9cM4ap AXwECA7B…7uyqxkcd AL7194fk…YNQBVjTB AZoyjqWo…cTWTRwva AeKNrjNj…1NEq95Ta

e85603b1938dd2…671e87d6b34472

1 in → 2 out7.1479 XPM225 B

AaFY9biw…5venTaoi ARZ9w5Nr…c8A4keKY

54ec2bf367f89b…66fdca83ec41bf

1 in → 2 out5.1055 XPM227 B

AQipjhzy…Dybz8YQg ATC87f3w…my2TFaqH

e4b5397a817c41…42a3bf7dd1ff12

1 in → 2 out3.0919 XPM227 B

ATg4oVom…awHZdScw AViGNKhn…R8HAjVai

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.

2.953 × 10⁹⁹(100-digit number)

29535393427677204654…15433536578478438399

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

2.953 × 10⁹⁹(100-digit number)

29535393427677204654…15433536578478438399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.953 × 10⁹⁹(100-digit number)

29535393427677204654…15433536578478438401

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

5.907 × 10⁹⁹(100-digit number)

59070786855354409309…30867073156956876799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.907 × 10⁹⁹(100-digit number)

59070786855354409309…30867073156956876801

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

1.181 × 10¹⁰⁰(101-digit number)

11814157371070881861…61734146313913753599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.181 × 10¹⁰⁰(101-digit number)

11814157371070881861…61734146313913753601

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

2.362 × 10¹⁰⁰(101-digit number)

23628314742141763723…23468292627827507199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.362 × 10¹⁰⁰(101-digit number)

23628314742141763723…23468292627827507201

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

4.725 × 10¹⁰⁰(101-digit number)

47256629484283527447…46936585255655014399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.725 × 10¹⁰⁰(101-digit number)

47256629484283527447…46936585255655014401

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