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Home/Chain Registry/Block #2,715,032

Block #2,715,032

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/21/2018, 1:46:46 PM Β· Difficulty 11.6117 Β· 4,127,125 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e67f58b2b520b123ff52f19d7ebe7d65b8ef07dda3cb294a92074c5c9310dc74
View on Chainz β†—

Difficulty

11.611702

Transactions

1

Size

199 B

Version

2

Bits

0b9c9881

Nonce

1,625,497,919

Timestamp

6/21/2018, 1:46:46 PM

Confirmations

4,127,125

Merkle Root

f166b5f23a143914315f238813c6e0cc492124a4fe7a97daebc313e2173ee05e
Transactions (1)
Coinbasef166b5f23a1439…c313e2173ee05e
1 in β†’ 1 out7.4000 XPM109 B
AS4P4GM1…2ah2dHdx
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.

2.863 Γ— 10⁹⁡(96-digit number)
28638940298435804354…83561799291985817600
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
2.863 Γ— 10⁹⁡(96-digit number)
28638940298435804354…83561799291985817601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.727 Γ— 10⁹⁡(96-digit number)
57277880596871608708…67123598583971635201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.145 Γ— 10⁹⁢(97-digit number)
11455576119374321741…34247197167943270401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.291 Γ— 10⁹⁢(97-digit number)
22911152238748643483…68494394335886540801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.582 Γ— 10⁹⁢(97-digit number)
45822304477497286966…36988788671773081601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.164 Γ— 10⁹⁢(97-digit number)
91644608954994573933…73977577343546163201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.832 Γ— 10⁹⁷(98-digit number)
18328921790998914786…47955154687092326401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.665 Γ— 10⁹⁷(98-digit number)
36657843581997829573…95910309374184652801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.331 Γ— 10⁹⁷(98-digit number)
73315687163995659146…91820618748369305601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.466 Γ— 10⁹⁸(99-digit number)
14663137432799131829…83641237496738611201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.932 Γ— 10⁹⁸(99-digit number)
29326274865598263658…67282474993477222401
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 2715032

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 e67f58b2b520b123ff52f19d7ebe7d65b8ef07dda3cb294a92074c5c9310dc74

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 #2,715,032 on Chainz β†—
Circulating Supply:57,981,646 XPMΒ·at block #6,842,156 Β· updates every 60s
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