Block #479,723

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/7/2014, 9:01:01 PM · Difficulty 10.5093 · 6,326,155 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a16198cc4be60478f518fed148e23019dc53378136c15f285441c4af1e5f5e9b

View on Chainz ↗

Height

#479,723

Difficulty

10.509254

Transactions

Size

1.15 KB

Version

Bits

0a825e7b

Nonce

19,960

Timestamp

4/7/2014, 9:01:01 PM

Confirmations

6,326,155

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

2c1a33405ec313be0ee7d139a1d9d7dc821a9b76275d2313288d5d6714c88dbe

Transactions (2)

Coinbase1315a53f2a6210…211344c0e30cdc

1 in → 1 out9.0500 XPM116 B

AbwWkWZt…kawDhufa

e16528958a8bb4…59abce6b6c176b

6 in → 2 out30.4486 XPM967 B

AXSFSLWS…ivo6FeWf AVy2XbU1…DgL7PfPk

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.

9.219 × 10⁹⁹(100-digit number)

92193241436384247528…57854352318194273039

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

9.219 × 10⁹⁹(100-digit number)

92193241436384247528…57854352318194273039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.219 × 10⁹⁹(100-digit number)

92193241436384247528…57854352318194273041

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

1.843 × 10¹⁰⁰(101-digit number)

18438648287276849505…15708704636388546079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.843 × 10¹⁰⁰(101-digit number)

18438648287276849505…15708704636388546081

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

3.687 × 10¹⁰⁰(101-digit number)

36877296574553699011…31417409272777092159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.687 × 10¹⁰⁰(101-digit number)

36877296574553699011…31417409272777092161

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

7.375 × 10¹⁰⁰(101-digit number)

73754593149107398023…62834818545554184319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.375 × 10¹⁰⁰(101-digit number)

73754593149107398023…62834818545554184321

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

1.475 × 10¹⁰¹(102-digit number)

14750918629821479604…25669637091108368639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.475 × 10¹⁰¹(102-digit number)

14750918629821479604…25669637091108368641

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