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Home/Chain Registry/Block #2,634,112

Block #2,634,112

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 6:37:08 PM Β· Difficulty 11.2234 Β· 4,199,329 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
de285ab957dea12e87255965c2d2ab661b9be705c48b1267c298d4289afa05e0
View on Chainz β†—

Difficulty

11.223352

Transactions

1

Size

201 B

Version

2

Bits

0b392d92

Nonce

2,110,655,030

Timestamp

4/28/2018, 6:37:08 PM

Confirmations

4,199,329

Merkle Root

8fdbf7965e733ddbb1d9c879c2dcb6d008603c67b3c6539dbbc6225bb462b231
Transactions (1)
Coinbase8fdbf7965e733d…c6225bb462b231
1 in β†’ 1 out7.9300 XPM110 B
AUdCEMd9…vUUCJcZr
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.714 Γ— 10⁹⁢(97-digit number)
57146969444110349664…46042804893208473600
Discovered Prime Numbers
p_k = 2^k Γ— 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.

1
origin + 1
5.714 Γ— 10⁹⁢(97-digit number)
57146969444110349664…46042804893208473601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.142 Γ— 10⁹⁷(98-digit number)
11429393888822069932…92085609786416947201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.285 Γ— 10⁹⁷(98-digit number)
22858787777644139865…84171219572833894401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.571 Γ— 10⁹⁷(98-digit number)
45717575555288279731…68342439145667788801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.143 Γ— 10⁹⁷(98-digit number)
91435151110576559463…36684878291335577601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.828 Γ— 10⁹⁸(99-digit number)
18287030222115311892…73369756582671155201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.657 Γ— 10⁹⁸(99-digit number)
36574060444230623785…46739513165342310401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.314 Γ— 10⁹⁸(99-digit number)
73148120888461247571…93479026330684620801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.462 Γ— 10⁹⁹(100-digit number)
14629624177692249514…86958052661369241601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.925 Γ— 10⁹⁹(100-digit number)
29259248355384499028…73916105322738483201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.851 Γ— 10⁹⁹(100-digit number)
58518496710768998056…47832210645476966401
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” 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 β†’
β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2634112

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 de285ab957dea12e87255965c2d2ab661b9be705c48b1267c298d4289afa05e0

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 β†’ Debug Window β†’ 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 #2,634,112 on Chainz β†—
Circulating Supply:57,911,725 XPMΒ·at block #6,833,440 Β· updates every 60s
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