Home/Chain Registry/Block #2,649,922

Block #2,649,922

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/5/2018, 3:23:30 PM · Difficulty 11.7606 · 4,187,684 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ce460bed3f9d394b588afde7fbe873e45250f55ad6848a933d2ad50a61ce2854

View on Chainz ↗

Height

#2,649,922

Difficulty

11.760644

Transactions

Size

882 B

Version

Bits

0bc2b990

Nonce

12,795,188

Timestamp

5/5/2018, 3:23:30 PM

Confirmations

4,187,684

Merkle Root

28b5f6d9bd88f37ce9ff21a8dfc052f83badec0fd67608c2c99a22b1caaf4f3a

Transactions (3)

Coinbase7fb6513668bb2d…b789f30138d166

1 in → 1 out7.2400 XPM110 B

AcFKfCAQ…88FKkRsU

42b4f59704c2aa…4f7f364821f63e

2 in → 2 out10.5250 XPM340 B

AVvgHwJr…kj4Gjujc AHTY4vSU…YSBm92Vr

d22c4be7475289…7de0747a6ddd39

2 in → 2 out11.6700 XPM342 B

AeS5XKw9…HJJqsvs1 Aa5Nd5pW…c6s4pbGF

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.

1.152 × 10⁹⁵(96-digit number)

11523805425993884894…48426825752546981480

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

1.152 × 10⁹⁵(96-digit number)

11523805425993884894…48426825752546981481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.304 × 10⁹⁵(96-digit number)

23047610851987769788…96853651505093962961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.609 × 10⁹⁵(96-digit number)

46095221703975539577…93707303010187925921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.219 × 10⁹⁵(96-digit number)

92190443407951079155…87414606020375851841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.843 × 10⁹⁶(97-digit number)

18438088681590215831…74829212040751703681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.687 × 10⁹⁶(97-digit number)

36876177363180431662…49658424081503407361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.375 × 10⁹⁶(97-digit number)

73752354726360863324…99316848163006814721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.475 × 10⁹⁷(98-digit number)

14750470945272172664…98633696326013629441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.950 × 10⁹⁷(98-digit number)

29500941890544345329…97267392652027258881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.900 × 10⁹⁷(98-digit number)

59001883781088690659…94534785304054517761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

1.180 × 10⁹⁸(99-digit number)

11800376756217738131…89069570608109035521

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 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

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 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 2649922

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 ce460bed3f9d394b588afde7fbe873e45250f55ad6848a933d2ad50a61ce2854

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 #2,649,922 on Chainz ↗

Block #2,649,922

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