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Home/Chain Registry/Block #2,102,267

Block #2,102,267

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/6/2017, 4:04:41 AM Β· Difficulty 10.8679 Β· 4,739,165 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0797841d05c6b51682db578a0d75ccd3885d4c60559e0c28e3d92a3137d04d42
View on Chainz β†—

Difficulty

10.867917

Transactions

1

Size

199 B

Version

2

Bits

0ade2fd0

Nonce

186,610,711

Timestamp

5/6/2017, 4:04:41 AM

Confirmations

4,739,165

Merkle Root

5fcee23eb69fd02ba534b32661c3b390bf29cd44d2e0e153c08e9f405b4fedc1
Transactions (1)
Coinbase5fcee23eb69fd0…8e9f405b4fedc1
1 in β†’ 1 out8.4500 XPM109 B
AHu8qTnr…iLumsfw4
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.

5.027 Γ— 10⁹⁴(95-digit number)
50275634580886186137…29281579013014773120
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
5.027 Γ— 10⁹⁴(95-digit number)
50275634580886186137…29281579013014773121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.005 Γ— 10⁹⁡(96-digit number)
10055126916177237227…58563158026029546241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.011 Γ— 10⁹⁡(96-digit number)
20110253832354474454…17126316052059092481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.022 Γ— 10⁹⁡(96-digit number)
40220507664708948909…34252632104118184961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.044 Γ— 10⁹⁡(96-digit number)
80441015329417897819…68505264208236369921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.608 Γ— 10⁹⁢(97-digit number)
16088203065883579563…37010528416472739841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.217 Γ— 10⁹⁢(97-digit number)
32176406131767159127…74021056832945479681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.435 Γ— 10⁹⁢(97-digit number)
64352812263534318255…48042113665890959361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.287 Γ— 10⁹⁷(98-digit number)
12870562452706863651…96084227331781918721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.574 Γ— 10⁹⁷(98-digit number)
25741124905413727302…92168454663563837441
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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 2102267

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 0797841d05c6b51682db578a0d75ccd3885d4c60559e0c28e3d92a3137d04d42

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 #2,102,267 on Chainz β†—
Circulating Supply:57,975,834 XPMΒ·at block #6,841,431 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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