Block #444,004

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/14/2014, 11:07:20 PM · Difficulty 10.3451 · 6,357,551 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8fd54bfd939f8ecf953e1ec6529fbb34ced6e35a3abeeb0e99e3a03b2e5a7434

View on Chainz ↗

Height

#444,004

Difficulty

10.345110

Transactions

Size

1.48 KB

Version

Bits

0a585929

Nonce

222,328

Timestamp

3/14/2014, 11:07:20 PM

Confirmations

6,357,551

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

795c8125bea48df7f889cd54083f2cad3561d2898c9a4808da45a01b622fe75e

Transactions (3)

Coinbase5bcd6ee48f171e…9423283a14f6aa

1 in → 1 out9.3600 XPM110 B

AeKNrjNj…1NEq95Ta

bd0462829a6408…164f005af47737

1 in → 2 out499.9900 XPM226 B

ATxd7QZe…ANRzaeah AUefe9ic…GEZQGisK

598b95890ee61f…aba45759a6229b

5 in → 14 out41.6910 XPM1.06 KB

ARWzDW5v…q24ajw2h AbJAcEfw…PkVprLzT AcTicBAM…U7PNLeDK AL5wNHbW…dFU2npvz Aadmiddm…LJWEuHig

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.

2.531 × 10¹⁰³(104-digit number)

25315556107786601837…34519302012566424959

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

2.531 × 10¹⁰³(104-digit number)

25315556107786601837…34519302012566424959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.531 × 10¹⁰³(104-digit number)

25315556107786601837…34519302012566424961

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

5.063 × 10¹⁰³(104-digit number)

50631112215573203675…69038604025132849919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.063 × 10¹⁰³(104-digit number)

50631112215573203675…69038604025132849921

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

1.012 × 10¹⁰⁴(105-digit number)

10126222443114640735…38077208050265699839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.012 × 10¹⁰⁴(105-digit number)

10126222443114640735…38077208050265699841

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

2.025 × 10¹⁰⁴(105-digit number)

20252444886229281470…76154416100531399679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.025 × 10¹⁰⁴(105-digit number)

20252444886229281470…76154416100531399681

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

4.050 × 10¹⁰⁴(105-digit number)

40504889772458562940…52308832201062799359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.050 × 10¹⁰⁴(105-digit number)

40504889772458562940…52308832201062799361

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