Block #474,305

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2014, 12:08:52 PM · Difficulty 10.4490 · 6,327,832 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4875e4d8f20300a7294a8d4cbae1c8ceaac88210ec72e54deb66a1cea29a3dc0

View on Chainz ↗

Height

#474,305

Difficulty

10.449011

Transactions

Size

2.06 KB

Version

Bits

0a72f268

Nonce

14,963

Timestamp

4/4/2014, 12:08:52 PM

Confirmations

6,327,832

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

88a575a402b35c9658a4db970bb39408a611d7c28ddbb1f1249fdd48625ef1dc

Transactions (4)

Coinbase9ca8a3b44c3912…029861cd7a7b6a

1 in → 1 out9.1800 XPM116 B

AbwWkWZt…kawDhufa

b86413f2685446…3c882a9fafc7f7

1 in → 2 out10.0100 XPM225 B

AUuyKcwM…i4PkvUrW AVqQ8PPb…y5xghjGM

4de428a40e701a…e2baed08648cf0

1 in → 2 out9.2000 XPM191 B

Aa4SCWnx…whoYHXDp ATx8iQ8h…XbxyuQRB

785526cfd5229f…c99bbd5403f0c8

7 in → 20 out64.1945 XPM1.45 KB

ASUi8WJ5…rcjzJnmE AZBgp11g…CPJiApFR AMnNFUVt…um9Nn6ba AL48EMca…MMV6JRSc AeKNrjNj…1NEq95Ta

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.

2.282 × 10¹⁰¹(102-digit number)

22827789313474752395…79146818986959195519

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

2.282 × 10¹⁰¹(102-digit number)

22827789313474752395…79146818986959195519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.282 × 10¹⁰¹(102-digit number)

22827789313474752395…79146818986959195521

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

4.565 × 10¹⁰¹(102-digit number)

45655578626949504790…58293637973918391039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.565 × 10¹⁰¹(102-digit number)

45655578626949504790…58293637973918391041

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

9.131 × 10¹⁰¹(102-digit number)

91311157253899009581…16587275947836782079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.131 × 10¹⁰¹(102-digit number)

91311157253899009581…16587275947836782081

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

1.826 × 10¹⁰²(103-digit number)

18262231450779801916…33174551895673564159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.826 × 10¹⁰²(103-digit number)

18262231450779801916…33174551895673564161

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

3.652 × 10¹⁰²(103-digit number)

36524462901559603832…66349103791347128319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.652 × 10¹⁰²(103-digit number)

36524462901559603832…66349103791347128321

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