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Block #522,859

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2014, 6:52:52 AM · Difficulty 10.8691 · 6,304,311 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

09406adc861affe2d7cd84a40cf6a7c48a9e3d6a455da2700fc854598f250a70

View on Chainz ↗

Height

#522,859

Difficulty

10.869123

Transactions

Size

1.04 KB

Version

Bits

0ade7edc

Nonce

7,679

Timestamp

5/3/2014, 6:52:52 AM

Confirmations

6,304,311

Merkle Root

4de7f734db76a5eec8178063f9bfabe56dbe02c3b1e3b5cf54f650997dfc4b5a

Transactions (2)

Coinbased5f0095358aef1…7c2eb98e5060ed

1 in → 20 out8.4600 XPM743 B

AGz9gyZW…bo8NYQpw AMW1p9oT…2TzdaZxH AbPcCMg4…719q6mAX AMVf7Jrg…xd5AVR7C AUzEPJFG…kYkA5U9V

1a9b0a4b8bb598…bc345ee27c555c

1 in → 2 out8.4600 XPM227 B

AaZB5Hon…x5uoebG7 AM8GuxnN…AfjbhWoV

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.

8.551 × 10⁹⁷(98-digit number)

85510704303839577473…78796178324272337920

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

8.551 × 10⁹⁷(98-digit number)

85510704303839577473…78796178324272337919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.551 × 10⁹⁷(98-digit number)

85510704303839577473…78796178324272337921

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

1.710 × 10⁹⁸(99-digit number)

17102140860767915494…57592356648544675839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.710 × 10⁹⁸(99-digit number)

17102140860767915494…57592356648544675841

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

3.420 × 10⁹⁸(99-digit number)

34204281721535830989…15184713297089351679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.420 × 10⁹⁸(99-digit number)

34204281721535830989…15184713297089351681

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

6.840 × 10⁹⁸(99-digit number)

68408563443071661979…30369426594178703359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.840 × 10⁹⁸(99-digit number)

68408563443071661979…30369426594178703361

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

1.368 × 10⁹⁹(100-digit number)

13681712688614332395…60738853188357406719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.368 × 10⁹⁹(100-digit number)

13681712688614332395…60738853188357406721

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

2.736 × 10⁹⁹(100-digit number)

27363425377228664791…21477706376714813439

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.

View full Prime Chain Discovery page →

★★★☆☆

Rarity

RareChain length 11

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 522859

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 09406adc861affe2d7cd84a40cf6a7c48a9e3d6a455da2700fc854598f250a70

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #522,859 on Chainz ↗

Block #522,859

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