Home/Chain Registry/Block #199,570

Block #199,570

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/8/2013, 11:17:32 AM · Difficulty 9.8877 · 6,613,250 confirmations

2CC

Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header

Block Hash

12e62ff1ea6b32ec8b58bffc3bc985b6e7944db7d03d393476e331a9749c997d

View on Chainz ↗

Height

#199,570

Difficulty

9.887745

Transactions

Size

1.07 KB

Version

Bits

09e34342

Nonce

3,792

Timestamp

10/8/2013, 11:17:32 AM

Confirmations

6,613,250

Merkle Root

e4af396f0ac23611ee9d0c00dfd70534dc34343f699d26bcf374a3bd743e7c64

Transactions (4)

Coinbase3281c61d98ce96…8011c254c4fe73

1 in → 1 out10.2400 XPM109 B

ATQzmnwG…XXhSDNtu

441d33f064f962…18c7eec7366cb9

1 in → 2 out10.2200 XPM225 B

AQgWZj2W…awiq9aJN AMfSRbun…y2GB5ED6

ead1e5671f5d77…5a7109e76c5d3a

1 in → 3 out10.2200 XPM227 B

AQXUSoBL…CzbjKp8b ANvtpRa1…QjsraDJz Ac5sZcdP…kzV4eckG

dfc79d47a1a84a…d9dee5e0167e7c

2 in → 5 out14.8842 XPM443 B

AcADmAoe…8iNnoMzB ANxERLYc…v7fC1vqc ANvtpRa1…QjsraDJz AQXUSoBL…CzbjKp8b ALXnWdQE…BBQNdhFQ

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.

2.537 × 10⁹³(94-digit number)

25370427341377246177…09094160441740121460

Discovered Prime Numbers

p_k = 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.

origin + 1

2.537 × 10⁹³(94-digit number)

25370427341377246177…09094160441740121461

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.074 × 10⁹³(94-digit number)

50740854682754492354…18188320883480242921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.014 × 10⁹⁴(95-digit number)

10148170936550898470…36376641766960485841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.029 × 10⁹⁴(95-digit number)

20296341873101796941…72753283533920971681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.059 × 10⁹⁴(95-digit number)

40592683746203593883…45506567067841943361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.118 × 10⁹⁴(95-digit number)

81185367492407187766…91013134135683886721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.623 × 10⁹⁵(96-digit number)

16237073498481437553…82026268271367773441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.247 × 10⁹⁵(96-digit number)

32474146996962875106…64052536542735546881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.494 × 10⁹⁵(96-digit number)

64948293993925750213…28105073085471093761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.298 × 10⁹⁶(97-digit number)

12989658798785150042…56210146170942187521

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. 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

UncommonChain length 10

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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 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 199570

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 12e62ff1ea6b32ec8b58bffc3bc985b6e7944db7d03d393476e331a9749c997d

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 #199,570 on Chainz ↗

Block #199,570

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