XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,093,800

Block #2,093,800

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2017, 4:39:12 AM Β· Difficulty 10.8712 Β· 4,739,621 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0eda691a85bcc60d9a07647f6ddc3a978c1273291984ce18ab273dbfd5d75a5c
View on Chainz β†—

Difficulty

10.871205

Transactions

2

Size

2.11 KB

Version

2

Bits

0adf0748

Nonce

1,704,898,060

Timestamp

4/30/2017, 4:39:12 AM

Confirmations

4,739,621

Merkle Root

418672ac3e1582bee7d9445e3106d2da056cbb8b78cb311759f94ef41f50f9fa
Transactions (2)
Coinbase0fa1cbef26c768…fb2038df2eb958
1 in β†’ 1 out8.4800 XPM109 B
AP6Ms2iK…cmEGhour
aa7fe76bef05dc…5c62149c3017d6
13 in β†’ 1 out65.9031 XPM1.92 KB
AVuHuNVy…NkwHF5q1
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.

2.266 Γ— 10⁹⁴(95-digit number)
22661898450098953547…61212825312160086000
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
2.266 Γ— 10⁹⁴(95-digit number)
22661898450098953547…61212825312160086001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.532 Γ— 10⁹⁴(95-digit number)
45323796900197907094…22425650624320172001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.064 Γ— 10⁹⁴(95-digit number)
90647593800395814188…44851301248640344001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.812 Γ— 10⁹⁡(96-digit number)
18129518760079162837…89702602497280688001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.625 Γ— 10⁹⁡(96-digit number)
36259037520158325675…79405204994561376001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.251 Γ— 10⁹⁡(96-digit number)
72518075040316651350…58810409989122752001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.450 Γ— 10⁹⁢(97-digit number)
14503615008063330270…17620819978245504001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.900 Γ— 10⁹⁢(97-digit number)
29007230016126660540…35241639956491008001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.801 Γ— 10⁹⁢(97-digit number)
58014460032253321080…70483279912982016001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.160 Γ— 10⁹⁷(98-digit number)
11602892006450664216…40966559825964032001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2093800

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 0eda691a85bcc60d9a07647f6ddc3a978c1273291984ce18ab273dbfd5d75a5c

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 #2,093,800 on Chainz β†—
Circulating Supply:57,911,571 XPMΒ·at block #6,833,420 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