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Home/Chain Registry/Block #2,645,499

Block #2,645,499

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2018, 10:41:57 PM Β· Difficulty 11.7333 Β· 4,193,977 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7382d2d350d8b818c3d973774a1e1f51f210e2c9685ce2ebdfdc8ce073735724
View on Chainz β†—

Difficulty

11.733309

Transactions

1

Size

200 B

Version

2

Bits

0bbbba21

Nonce

663,205,797

Timestamp

5/2/2018, 10:41:57 PM

Confirmations

4,193,977

Merkle Root

b40c4ed255710f22722fe3f97e6304f0ea85db4d96510c7f9005e5f5f95be948
Transactions (1)
Coinbaseb40c4ed255710f…05e5f5f95be948
1 in β†’ 1 out7.2500 XPM110 B
AaeQwr8t…drFSM3hL
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.

3.332 Γ— 10⁹³(94-digit number)
33323913479634098626…36684295432524527200
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
3.332 Γ— 10⁹³(94-digit number)
33323913479634098626…36684295432524527201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.664 Γ— 10⁹³(94-digit number)
66647826959268197253…73368590865049054401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.332 Γ— 10⁹⁴(95-digit number)
13329565391853639450…46737181730098108801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.665 Γ— 10⁹⁴(95-digit number)
26659130783707278901…93474363460196217601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.331 Γ— 10⁹⁴(95-digit number)
53318261567414557803…86948726920392435201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.066 Γ— 10⁹⁡(96-digit number)
10663652313482911560…73897453840784870401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.132 Γ— 10⁹⁡(96-digit number)
21327304626965823121…47794907681569740801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.265 Γ— 10⁹⁡(96-digit number)
42654609253931646242…95589815363139481601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.530 Γ— 10⁹⁡(96-digit number)
85309218507863292485…91179630726278963201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.706 Γ— 10⁹⁢(97-digit number)
17061843701572658497…82359261452557926401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.412 Γ— 10⁹⁢(97-digit number)
34123687403145316994…64718522905115852801
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 2645499

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 7382d2d350d8b818c3d973774a1e1f51f210e2c9685ce2ebdfdc8ce073735724

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 #2,645,499 on Chainz β†—
Circulating Supply:57,960,101 XPMΒ·at block #6,839,475 Β· updates every 60s
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