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Home/Chain Registry/Block #2,187,464

Block #2,187,464

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/1/2017, 5:22:09 AM Β· Difficulty 10.9473 Β· 4,656,228 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
72bf2414be6ed6a16ceaee2632acce6cd1309cdf9bc208af00787eaa4bb2dcbb
View on Chainz β†—

Difficulty

10.947258

Transactions

3

Size

1.32 KB

Version

2

Bits

0af27f7c

Nonce

1,865,050,035

Timestamp

7/1/2017, 5:22:09 AM

Confirmations

4,656,228

Merkle Root

1051612a4464f3279e39b3a791798a6a46455872cc071cbe5c7c93f5f3e072b7
Transactions (3)
Coinbase6fb2b8fec29718…808dd7a8f7125e
1 in β†’ 1 out8.3700 XPM110 B
AW6DUkQd…6rGmjtqv
b0765826846a1d…1a602c62fcfd08
3 in β†’ 1 out2393.9900 XPM487 B
AeUhnKM5…KVHUaQNo
ce72bbd7bbee62…ef853d1eec5a7e
4 in β†’ 2 out697.0000 XPM668 B
AVFtFt7a…EGcrBsUAAcxhUhX6…N8N8w2tm
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.

5.626 Γ— 10⁹⁢(97-digit number)
56264141097174714664…03183426406313958400
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
5.626 Γ— 10⁹⁢(97-digit number)
56264141097174714664…03183426406313958401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.125 Γ— 10⁹⁷(98-digit number)
11252828219434942932…06366852812627916801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.250 Γ— 10⁹⁷(98-digit number)
22505656438869885865…12733705625255833601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.501 Γ— 10⁹⁷(98-digit number)
45011312877739771731…25467411250511667201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.002 Γ— 10⁹⁷(98-digit number)
90022625755479543463…50934822501023334401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.800 Γ— 10⁹⁸(99-digit number)
18004525151095908692…01869645002046668801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.600 Γ— 10⁹⁸(99-digit number)
36009050302191817385…03739290004093337601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.201 Γ— 10⁹⁸(99-digit number)
72018100604383634770…07478580008186675201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.440 Γ— 10⁹⁹(100-digit number)
14403620120876726954…14957160016373350401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.880 Γ— 10⁹⁹(100-digit number)
28807240241753453908…29914320032746700801
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 2187464

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 72bf2414be6ed6a16ceaee2632acce6cd1309cdf9bc208af00787eaa4bb2dcbb

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 #2,187,464 on Chainz β†—
Circulating Supply:57,993,903 XPMΒ·at block #6,843,691 Β· updates every 60s
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