Block #417,849

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/24/2014, 11:05:22 AM · Difficulty 10.3904 · 6,388,067 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bf6c1fe83ec2189493dd675c6d72bdfcf42d21424a5b162359e4a3e6eb43d25c

View on Chainz ↗

Height

#417,849

Difficulty

10.390394

Transactions

Size

903 B

Version

Bits

0a63f0d8

Nonce

216,622

Timestamp

2/24/2014, 11:05:22 AM

Confirmations

6,388,067

Mined by

⛏️ 9`aS'KBAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

3e18a1c600396d88da66a214ea4e33220e1260cc28e881e530aaa0aa3d2d026c

Transactions (1)

Coinbase3e18a1c600396d…aaa0aa3d2d026c

1 in → 22 out9.2500 XPM811 B

AQvZBsUo…hppgRZTJ AFutDVqJ…TJTJj6UF Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH

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.

1.591 × 10¹⁰⁰(101-digit number)

15916797664759320830…40028640156282921339

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

1.591 × 10¹⁰⁰(101-digit number)

15916797664759320830…40028640156282921339

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.591 × 10¹⁰⁰(101-digit number)

15916797664759320830…40028640156282921341

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

3.183 × 10¹⁰⁰(101-digit number)

31833595329518641661…80057280312565842679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.183 × 10¹⁰⁰(101-digit number)

31833595329518641661…80057280312565842681

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

6.366 × 10¹⁰⁰(101-digit number)

63667190659037283322…60114560625131685359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.366 × 10¹⁰⁰(101-digit number)

63667190659037283322…60114560625131685361

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

1.273 × 10¹⁰¹(102-digit number)

12733438131807456664…20229121250263370719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.273 × 10¹⁰¹(102-digit number)

12733438131807456664…20229121250263370721

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

2.546 × 10¹⁰¹(102-digit number)

25466876263614913328…40458242500526741439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.546 × 10¹⁰¹(102-digit number)

25466876263614913328…40458242500526741441

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