Block #473,316

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/3/2014, 7:46:51 PM · Difficulty 10.4473 · 6,324,315 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c4aefa9a0d81f73aa5bdfbed7e5704c3a7eb1b5fadfe580d11ff36e6a3172e49

View on Chainz ↗

Height

#473,316

Difficulty

10.447260

Transactions

Size

542 B

Version

Bits

0a727fa4

Nonce

270,314

Timestamp

4/3/2014, 7:46:51 PM

Confirmations

6,324,315

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

5507a9a557cd8b7d89a549960580a36b60e8536005831097d8623d3acbe724c5

Transactions (2)

Coinbasea0869e787189c2…56af433d350d29

1 in → 1 out9.1600 XPM110 B

AeKNrjNj…1NEq95Ta

9e6cdbbd83dfd6…1600fa0b6a8234

2 in → 1 out139.9900 XPM340 B

AN2473CQ…ZTAKqBYu

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.

1.590 × 10¹⁰⁰(101-digit number)

15908249267912689565…28626857937102522599

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

1.590 × 10¹⁰⁰(101-digit number)

15908249267912689565…28626857937102522599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.590 × 10¹⁰⁰(101-digit number)

15908249267912689565…28626857937102522601

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

3.181 × 10¹⁰⁰(101-digit number)

31816498535825379130…57253715874205045199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.181 × 10¹⁰⁰(101-digit number)

31816498535825379130…57253715874205045201

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

6.363 × 10¹⁰⁰(101-digit number)

63632997071650758260…14507431748410090399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.363 × 10¹⁰⁰(101-digit number)

63632997071650758260…14507431748410090401

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

1.272 × 10¹⁰¹(102-digit number)

12726599414330151652…29014863496820180799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.272 × 10¹⁰¹(102-digit number)

12726599414330151652…29014863496820180801

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

2.545 × 10¹⁰¹(102-digit number)

25453198828660303304…58029726993640361599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.545 × 10¹⁰¹(102-digit number)

25453198828660303304…58029726993640361601

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