XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #278,198

Block #278,198

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/27/2013, 9:26:28 PM Β· Difficulty 9.9683 Β· 6,522,421 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dc649e6f27fb6eab3b146e62ca0ca948e590e86bc2601e6b4f62a030fbc21c93
View on Chainz β†—

Height

#278,198

Difficulty

9.968313

Transactions

1

Size

200 B

Version

2

Bits

09f7e35f

Nonce

27,267

Timestamp

11/27/2013, 9:26:28 PM

Confirmations

6,522,421

Merkle Root

772e6387c985ab093533a464cd7e8dc759f164786194dd08d004555fb0b346ad
Transactions (1)
Coinbase772e6387c985ab…04555fb0b346ad
1 in β†’ 1 out10.0500 XPM109 B
AeKNrjNj…1NEq95Ta
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.

6.885 Γ— 10⁹⁡(96-digit number)
68851259064462514798…89014211634713352320
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
6.885 Γ— 10⁹⁡(96-digit number)
68851259064462514798…89014211634713352321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.377 Γ— 10⁹⁢(97-digit number)
13770251812892502959…78028423269426704641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.754 Γ— 10⁹⁢(97-digit number)
27540503625785005919…56056846538853409281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.508 Γ— 10⁹⁢(97-digit number)
55081007251570011838…12113693077706818561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.101 Γ— 10⁹⁷(98-digit number)
11016201450314002367…24227386155413637121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.203 Γ— 10⁹⁷(98-digit number)
22032402900628004735…48454772310827274241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.406 Γ— 10⁹⁷(98-digit number)
44064805801256009471…96909544621654548481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.812 Γ— 10⁹⁷(98-digit number)
88129611602512018942…93819089243309096961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.762 Γ— 10⁹⁸(99-digit number)
17625922320502403788…87638178486618193921
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 278198

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 dc649e6f27fb6eab3b146e62ca0ca948e590e86bc2601e6b4f62a030fbc21c93

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 #278,198 on Chainz β†—
Circulating Supply:57,649,014 XPMΒ·at block #6,800,618 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.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK