Block #491,843

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/14/2014, 6:10:03 PM · Difficulty 10.6856 · 6,311,800 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cb6cf496f4ec57d193830cd7d27b5c6b5cd5815387cc07790d0225aa0091e799

View on Chainz ↗

Height

#491,843

Difficulty

10.685601

Transactions

Size

887 B

Version

Bits

0aaf8390

Nonce

281,007,020

Timestamp

4/14/2014, 6:10:03 PM

Confirmations

6,311,800

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

ac208db22d37a568d184944e1a1fe6c87a8b440fc6e26f8c47690a4d90b1b426

Transactions (4)

Coinbasedc5f08b17e63cf…48cb52e3d142b6

1 in → 1 out8.7700 XPM116 B

AbwWkWZt…kawDhufa

a712bc01597592…f6b097592ac62d

1 in → 2 out6.7655 XPM226 B

ARBNrk9M…YTv4gMek AXRHxia8…RW4zoiGj

1f27d23103dacf…5fd7c95470be70

1 in → 2 out6.7366 XPM226 B

AdobpKjj…M9auVuzw ATtfFeMD…dAnB4xVW

5d5257f1f7dbf7…87993165f12b0d

1 in → 2 out6.7388 XPM227 B

ALKpXmxU…jhTppDrP AS4C9wru…QMZGuh62

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.

6.062 × 10⁹⁹(100-digit number)

60625925288781658817…79757724941528596479

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

6.062 × 10⁹⁹(100-digit number)

60625925288781658817…79757724941528596479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.062 × 10⁹⁹(100-digit number)

60625925288781658817…79757724941528596481

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

1.212 × 10¹⁰⁰(101-digit number)

12125185057756331763…59515449883057192959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.212 × 10¹⁰⁰(101-digit number)

12125185057756331763…59515449883057192961

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

2.425 × 10¹⁰⁰(101-digit number)

24250370115512663526…19030899766114385919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.425 × 10¹⁰⁰(101-digit number)

24250370115512663526…19030899766114385921

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

4.850 × 10¹⁰⁰(101-digit number)

48500740231025327053…38061799532228771839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.850 × 10¹⁰⁰(101-digit number)

48500740231025327053…38061799532228771841

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

9.700 × 10¹⁰⁰(101-digit number)

97001480462050654107…76123599064457543679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.700 × 10¹⁰⁰(101-digit number)

97001480462050654107…76123599064457543681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.940 × 10¹⁰¹(102-digit number)

19400296092410130821…52247198128915087359

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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