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Home/Chain Registry/Block #2,647,365

Block #2,647,365

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2018, 9:31:04 PM Β· Difficulty 11.7584 Β· 4,189,038 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6029faaddbb2f540170ac7190fcb0f90acab31cfea474ba2ae9184d944242e5b
View on Chainz β†—

Difficulty

11.758357

Transactions

1

Size

200 B

Version

2

Bits

0bc223af

Nonce

1,116,659,765

Timestamp

5/3/2018, 9:31:04 PM

Confirmations

4,189,038

Merkle Root

8bc29d9782e0f6904fa4c329ca1d890a0143de7fdbc86fe5855404877901facf
Transactions (1)
Coinbase8bc29d9782e0f6…5404877901facf
1 in β†’ 1 out7.2200 XPM110 B
AXKq7mVX…VbirbTho
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.

1.975 Γ— 10⁹⁡(96-digit number)
19753824610005947699…79077154690857656320
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
1.975 Γ— 10⁹⁡(96-digit number)
19753824610005947699…79077154690857656321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.950 Γ— 10⁹⁡(96-digit number)
39507649220011895398…58154309381715312641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.901 Γ— 10⁹⁡(96-digit number)
79015298440023790797…16308618763430625281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.580 Γ— 10⁹⁢(97-digit number)
15803059688004758159…32617237526861250561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.160 Γ— 10⁹⁢(97-digit number)
31606119376009516318…65234475053722501121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.321 Γ— 10⁹⁢(97-digit number)
63212238752019032637…30468950107445002241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.264 Γ— 10⁹⁷(98-digit number)
12642447750403806527…60937900214890004481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.528 Γ— 10⁹⁷(98-digit number)
25284895500807613055…21875800429780008961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.056 Γ— 10⁹⁷(98-digit number)
50569791001615226110…43751600859560017921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.011 Γ— 10⁹⁸(99-digit number)
10113958200323045222…87503201719120035841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.022 Γ— 10⁹⁸(99-digit number)
20227916400646090444…75006403438240071681
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 2647365

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 6029faaddbb2f540170ac7190fcb0f90acab31cfea474ba2ae9184d944242e5b

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 #2,647,365 on Chainz β†—
Circulating Supply:57,935,488 XPMΒ·at block #6,836,402 Β· updates every 60s
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