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Home/Chain Registry/Block #2,815,736

Block #2,815,736

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/29/2018, 7:35:41 PM Β· Difficulty 11.6844 Β· 4,027,357 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3246abb9070df19d46f97172f4bb71c99f93d81126ac5ecde2fec600c166fdd2
View on Chainz β†—

Difficulty

11.684414

Transactions

1

Size

201 B

Version

2

Bits

0baf35c1

Nonce

1,630,554,950

Timestamp

8/29/2018, 7:35:41 PM

Confirmations

4,027,357

Merkle Root

5eb741b6a54ae61e223efff21528c0079891e3ecace2c8e14d1d766b9b243ecd
Transactions (1)
Coinbase5eb741b6a54ae6…1d766b9b243ecd
1 in β†’ 1 out7.3100 XPM110 B
AZtxQr2F…7grUWrUz
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.

1.585 Γ— 10⁹⁢(97-digit number)
15857206311719325596…51591577609564067840
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
1.585 Γ— 10⁹⁢(97-digit number)
15857206311719325596…51591577609564067841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.171 Γ— 10⁹⁢(97-digit number)
31714412623438651192…03183155219128135681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.342 Γ— 10⁹⁢(97-digit number)
63428825246877302384…06366310438256271361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.268 Γ— 10⁹⁷(98-digit number)
12685765049375460476…12732620876512542721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.537 Γ— 10⁹⁷(98-digit number)
25371530098750920953…25465241753025085441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.074 Γ— 10⁹⁷(98-digit number)
50743060197501841907…50930483506050170881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.014 Γ— 10⁹⁸(99-digit number)
10148612039500368381…01860967012100341761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.029 Γ— 10⁹⁸(99-digit number)
20297224079000736763…03721934024200683521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.059 Γ— 10⁹⁸(99-digit number)
40594448158001473526…07443868048401367041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.118 Γ— 10⁹⁸(99-digit number)
81188896316002947052…14887736096802734081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.623 Γ— 10⁹⁹(100-digit number)
16237779263200589410…29775472193605468161
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 2815736

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 3246abb9070df19d46f97172f4bb71c99f93d81126ac5ecde2fec600c166fdd2

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 #2,815,736 on Chainz β†—
Circulating Supply:57,989,107 XPMΒ·at block #6,843,092 Β· updates every 60s
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