Block #362,729

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/16/2014, 9:46:06 PM · Difficulty 10.4178 · 6,436,756 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

efa327fd10e723dcd05054036edc07ed19f76fa306d4b6e6a67e4d48aefb6b29

View on Chainz ↗

Height

#362,729

Difficulty

10.417825

Transactions

Size

1.38 KB

Version

Bits

0a6af693

Nonce

9,890

Timestamp

1/16/2014, 9:46:06 PM

Confirmations

6,436,756

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

350ce2ec9e7b042c64a15420b46ef230159407e6c50a45581c1480e88fb34dce

Transactions (5)

Coinbasee3b2fb3afda0bf…6f0cd39e5b5f7a

1 in → 1 out9.2400 XPM116 B

AbwWkWZt…kawDhufa

3da6402b72bc4c…59f73bfc34be2f

1 in → 2 out9.2400 XPM226 B

AKmxBBzd…AHmu4uiE AMUweau9…QSDqtx6i

4f02fb57506f05…9799a518ef1743

1 in → 2 out9.2400 XPM227 B

AZMs6PQy…hxKsRcgB AXvPvpX8…r4euFFVs

d579d7f8a027f6…021ccd46b791f5

1 in → 2 out6.1062 XPM225 B

AdTUEozM…4cfe2d9A AGeiFFDo…SVzaxepL

afdda6dfad2423…f63327ee419e7d

3 in → 2 out2.0391 XPM522 B

AHrrAfZP…cWw9Zwvb AdhUErGY…P6SsFaVU

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.

1.436 × 10⁹⁹(100-digit number)

14362400115406527550…72730463102212459879

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

1.436 × 10⁹⁹(100-digit number)

14362400115406527550…72730463102212459879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.436 × 10⁹⁹(100-digit number)

14362400115406527550…72730463102212459881

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

2.872 × 10⁹⁹(100-digit number)

28724800230813055101…45460926204424919759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.872 × 10⁹⁹(100-digit number)

28724800230813055101…45460926204424919761

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

5.744 × 10⁹⁹(100-digit number)

57449600461626110203…90921852408849839519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.744 × 10⁹⁹(100-digit number)

57449600461626110203…90921852408849839521

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

1.148 × 10¹⁰⁰(101-digit number)

11489920092325222040…81843704817699679039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.148 × 10¹⁰⁰(101-digit number)

11489920092325222040…81843704817699679041

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

2.297 × 10¹⁰⁰(101-digit number)

22979840184650444081…63687409635399358079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.297 × 10¹⁰⁰(101-digit number)

22979840184650444081…63687409635399358081

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