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Home/Chain Registry/Block #2,642,864

Block #2,642,864

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 9:36:32 PM Β· Difficulty 11.6661 Β· 4,189,820 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2d22ffe8d4975cd5aae908ccec1ce2026cdf7850c831b67c09b9cffd5502f0f5
View on Chainz β†—

Difficulty

11.666132

Transactions

1

Size

200 B

Version

2

Bits

0baa87a1

Nonce

286,362,272

Timestamp

5/1/2018, 9:36:32 PM

Confirmations

4,189,820

Merkle Root

5121bdcee41f9c0482f747298c23356759803c5bd4270a782689dcac24bad0b6
Transactions (1)
Coinbase5121bdcee41f9c…89dcac24bad0b6
1 in β†’ 1 out7.3400 XPM110 B
Ac7amKhH…qgr6Skp8
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.

3.024 Γ— 10⁹⁴(95-digit number)
30243247620448098317…52793675015109585960
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
3.024 Γ— 10⁹⁴(95-digit number)
30243247620448098317…52793675015109585961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.048 Γ— 10⁹⁴(95-digit number)
60486495240896196634…05587350030219171921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.209 Γ— 10⁹⁡(96-digit number)
12097299048179239326…11174700060438343841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.419 Γ— 10⁹⁡(96-digit number)
24194598096358478653…22349400120876687681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.838 Γ— 10⁹⁡(96-digit number)
48389196192716957307…44698800241753375361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.677 Γ— 10⁹⁡(96-digit number)
96778392385433914615…89397600483506750721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.935 Γ— 10⁹⁢(97-digit number)
19355678477086782923…78795200967013501441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.871 Γ— 10⁹⁢(97-digit number)
38711356954173565846…57590401934027002881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.742 Γ— 10⁹⁢(97-digit number)
77422713908347131692…15180803868054005761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.548 Γ— 10⁹⁷(98-digit number)
15484542781669426338…30361607736108011521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.096 Γ— 10⁹⁷(98-digit number)
30969085563338852676…60723215472216023041
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 2642864

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 2d22ffe8d4975cd5aae908ccec1ce2026cdf7850c831b67c09b9cffd5502f0f5

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 #2,642,864 on Chainz β†—
Circulating Supply:57,905,627 XPMΒ·at block #6,832,683 Β· updates every 60s
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