XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,855,604

Block #2,855,604

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/26/2018, 8:45:02 AM Β· Difficulty 11.6980 Β· 3,977,888 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3b6ad62000d5140cc1929968a16813d9da7ddbbed0d25076243745ef6e0afdcd
View on Chainz β†—

Difficulty

11.698030

Transactions

1

Size

201 B

Version

2

Bits

0bb2b21d

Nonce

661,544,068

Timestamp

9/26/2018, 8:45:02 AM

Confirmations

3,977,888

Merkle Root

4918ebe7599830575eed1ab679bf177fb71d0c00427bdd2062a13fd2d8ba4ae8
Transactions (1)
Coinbase4918ebe7599830…a13fd2d8ba4ae8
1 in β†’ 1 out7.3000 XPM110 B
AUMQRepm…tAfKmdW1
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.

3.069 Γ— 10⁹⁢(97-digit number)
30693645845057199747…91141389687074437120
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
3.069 Γ— 10⁹⁢(97-digit number)
30693645845057199747…91141389687074437121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.138 Γ— 10⁹⁢(97-digit number)
61387291690114399494…82282779374148874241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.227 Γ— 10⁹⁷(98-digit number)
12277458338022879898…64565558748297748481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.455 Γ— 10⁹⁷(98-digit number)
24554916676045759797…29131117496595496961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.910 Γ— 10⁹⁷(98-digit number)
49109833352091519595…58262234993190993921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.821 Γ— 10⁹⁷(98-digit number)
98219666704183039190…16524469986381987841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.964 Γ— 10⁹⁸(99-digit number)
19643933340836607838…33048939972763975681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.928 Γ— 10⁹⁸(99-digit number)
39287866681673215676…66097879945527951361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.857 Γ— 10⁹⁸(99-digit number)
78575733363346431352…32195759891055902721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.571 Γ— 10⁹⁹(100-digit number)
15715146672669286270…64391519782111805441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.143 Γ— 10⁹⁹(100-digit number)
31430293345338572541…28783039564223610881
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 2855604

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 3b6ad62000d5140cc1929968a16813d9da7ddbbed0d25076243745ef6e0afdcd

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 #2,855,604 on Chainz β†—
Circulating Supply:57,912,142 XPMΒ·at block #6,833,491 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy