Block #509,410

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/25/2014, 12:47:58 AM · Difficulty 10.8206 · 6,291,618 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c1bde7d1ea5810465b0705e01c5dede153c12e12454f87c63bdbe24cb438e8c0

View on Chainz ↗

Height

#509,410

Difficulty

10.820579

Transactions

Size

3.04 KB

Version

Bits

0ad21176

Nonce

203,366

Timestamp

4/25/2014, 12:47:58 AM

Confirmations

6,291,618

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

440cdeff73577073870fcc0ac33d56a53be2ddb50b0e1839c46c251f0dfd80dc

Transactions (4)

Coinbaseb35f283b0dfe38…3a032bdf6fd0ee

1 in → 1 out8.5800 XPM116 B

AbwWkWZt…kawDhufa

bd2e6bf63379ab…4539a8b2785e48

16 in → 2 out15.2414 XPM2.39 KB

AViiRDH8…7sQzHarU AZSjhnMj…Mnf3y9ki

51bf94540a15fb…5f98f7211269ec

1 in → 2 out1.2745 XPM226 B

AJn3eGzy…upQ9s6Z9 AGdWVjRk…LFVsqCnK

02d10a73acbd51…e11d16df7c21d1

1 in → 2 out1.1718 XPM226 B

ASGoUfHB…eDgFu5yk AeJjXXhd…cyHLXSKP

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.

1.355 × 10¹⁰⁰(101-digit number)

13556327821511966178…67190684775729766399

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

1.355 × 10¹⁰⁰(101-digit number)

13556327821511966178…67190684775729766399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.355 × 10¹⁰⁰(101-digit number)

13556327821511966178…67190684775729766401

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

2.711 × 10¹⁰⁰(101-digit number)

27112655643023932356…34381369551459532799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.711 × 10¹⁰⁰(101-digit number)

27112655643023932356…34381369551459532801

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

5.422 × 10¹⁰⁰(101-digit number)

54225311286047864713…68762739102919065599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.422 × 10¹⁰⁰(101-digit number)

54225311286047864713…68762739102919065601

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

1.084 × 10¹⁰¹(102-digit number)

10845062257209572942…37525478205838131199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.084 × 10¹⁰¹(102-digit number)

10845062257209572942…37525478205838131201

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

2.169 × 10¹⁰¹(102-digit number)

21690124514419145885…75050956411676262399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.169 × 10¹⁰¹(102-digit number)

21690124514419145885…75050956411676262401

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