Block #401,578

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/12/2014, 8:55:42 PM · Difficulty 10.4333 · 6,412,810 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

16113259bd1b5c25bde95a4f3a0ad718d218c2182b411ddac86309db894adab7

View on Chainz ↗

Height

#401,578

Difficulty

10.433270

Transactions

Size

1005 B

Version

Bits

0a6eeac3

Nonce

23,724

Timestamp

2/12/2014, 8:55:42 PM

Confirmations

6,412,810

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

15fff49c31cc542300047d8df45d3c3a8be53827fe998b4b5e266dd487181908

Transactions (1)

Coinbase15fff49c31cc54…266dd487181908

1 in → 25 out9.1700 XPM913 B

AQvZBsUo…hppgRZTJ Af76ewER…EzGhbQ6S AGKhfQo2…h7fBXLX6 Aac9Hjdg…P4ktypc3 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.

2.936 × 10¹⁰⁰(101-digit number)

29366548450286290242…46317572323888665599

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

2.936 × 10¹⁰⁰(101-digit number)

29366548450286290242…46317572323888665599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.936 × 10¹⁰⁰(101-digit number)

29366548450286290242…46317572323888665601

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

5.873 × 10¹⁰⁰(101-digit number)

58733096900572580484…92635144647777331199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.873 × 10¹⁰⁰(101-digit number)

58733096900572580484…92635144647777331201

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

1.174 × 10¹⁰¹(102-digit number)

11746619380114516096…85270289295554662399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.174 × 10¹⁰¹(102-digit number)

11746619380114516096…85270289295554662401

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

2.349 × 10¹⁰¹(102-digit number)

23493238760229032193…70540578591109324799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.349 × 10¹⁰¹(102-digit number)

23493238760229032193…70540578591109324801

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

4.698 × 10¹⁰¹(102-digit number)

46986477520458064387…41081157182218649599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.698 × 10¹⁰¹(102-digit number)

46986477520458064387…41081157182218649601

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

Block #401,578

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