Home/Chain Registry/Block #2,657,508

Block #2,657,508

2CCLength 12★★★★☆

Cunningham Chain of the Second Kind · Discovered 5/12/2018, 1:35:02 AM · Difficulty 11.6675 · 4,174,421 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

0124df6ad689c69e29caa2a4cc772c5f27ab6b027c5f4f058a4a5c1df3f6932e

View on Chainz ↗

Height

#2,657,508

Difficulty

11.667545

Transactions

Size

1.99 KB

Version

Bits

0baae435

Nonce

1,889,333,019

Timestamp

5/12/2018, 1:35:02 AM

Confirmations

4,174,421

Merkle Root

40eca91563bf3f7f5fe06b32fcc176bbb2c50de088471a3de6ceb0a65f9a054c

Transactions (4)

Coinbasef8b7a9af08a933…704849f3a531cf

1 in → 1 out7.3600 XPM109 B

APw7A9eM…yC82dMnB

1ce78682cd36a1…d15e81cc680764

1 in → 2 out7.2300 XPM192 B

AdKhEL4Q…RQS9ZydR ASpavcsP…N93QxZ1S

c736c80fc9e748…729f7a814d8203

5 in → 2 out49.9900 XPM821 B

ALjLjYzh…ehX7Jx55 AdEoGAhM…QAMbxftD

e15831e4ca3e4a…e5880afe9525a1

6 in → 2 out34.4916 XPM829 B

AWp4iAg7…FUBLEm8x AaEySbYz…KBMGPtGM

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.

1.979 × 10⁹⁴(95-digit number)

19798000468644338602…52591669571124757840

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

1.979 × 10⁹⁴(95-digit number)

19798000468644338602…52591669571124757841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.959 × 10⁹⁴(95-digit number)

39596000937288677205…05183339142249515681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.919 × 10⁹⁴(95-digit number)

79192001874577354411…10366678284499031361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.583 × 10⁹⁵(96-digit number)

15838400374915470882…20733356568998062721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.167 × 10⁹⁵(96-digit number)

31676800749830941764…41466713137996125441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.335 × 10⁹⁵(96-digit number)

63353601499661883528…82933426275992250881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.267 × 10⁹⁶(97-digit number)

12670720299932376705…65866852551984501761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.534 × 10⁹⁶(97-digit number)

25341440599864753411…31733705103969003521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.068 × 10⁹⁶(97-digit number)

50682881199729506823…63467410207938007041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.013 × 10⁹⁷(98-digit number)

10136576239945901364…26934820415876014081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

2.027 × 10⁹⁷(98-digit number)

20273152479891802729…53869640831752028161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^11 × origin + 1

4.054 × 10⁹⁷(98-digit number)

40546304959783605458…07739281663504056321

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

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 2657508

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 0124df6ad689c69e29caa2a4cc772c5f27ab6b027c5f4f058a4a5c1df3f6932e

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 #2,657,508 on Chainz ↗

Block #2,657,508

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