Block #436,018

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/9/2014, 8:03:26 AM · Difficulty 10.3549 · 6,367,688 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

30289ebcc06165d04735db7e0a6d02f73062c8b7f1559bae497d1214fffbaaaa

View on Chainz ↗

Height

#436,018

Difficulty

10.354928

Transactions

Size

903 B

Version

Bits

0a5adc91

Nonce

35,830

Timestamp

3/9/2014, 8:03:26 AM

Confirmations

6,367,688

Mined by

⛏️ 2aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e9955780adb71b576a3bd46bfd2134a434cf9e547b97fe39451852779275213a

Transactions (1)

Coinbasee9955780adb71b…1852779275213a

1 in → 22 out9.3100 XPM811 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGD4yZQw…hGzM2XAx AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

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.

5.028 × 10⁹⁹(100-digit number)

50282083667024383954…79802729713825374079

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

5.028 × 10⁹⁹(100-digit number)

50282083667024383954…79802729713825374079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.028 × 10⁹⁹(100-digit number)

50282083667024383954…79802729713825374081

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

1.005 × 10¹⁰⁰(101-digit number)

10056416733404876790…59605459427650748159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.005 × 10¹⁰⁰(101-digit number)

10056416733404876790…59605459427650748161

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

2.011 × 10¹⁰⁰(101-digit number)

20112833466809753581…19210918855301496319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.011 × 10¹⁰⁰(101-digit number)

20112833466809753581…19210918855301496321

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

4.022 × 10¹⁰⁰(101-digit number)

40225666933619507163…38421837710602992639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.022 × 10¹⁰⁰(101-digit number)

40225666933619507163…38421837710602992641

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

8.045 × 10¹⁰⁰(101-digit number)

80451333867239014326…76843675421205985279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.045 × 10¹⁰⁰(101-digit number)

80451333867239014326…76843675421205985281

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