XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,610,766

Block #2,610,766

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/12/2018, 1:57:56 PM Β· Difficulty 11.2184 Β· 4,222,734 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d24adc41a3d92af75a02f7ca2599c5eb3f493f21373733db6e5c21bf3d7a3767
View on Chainz β†—

Difficulty

11.218395

Transactions

1

Size

200 B

Version

2

Bits

0b37e8c3

Nonce

779,547,841

Timestamp

4/12/2018, 1:57:56 PM

Confirmations

4,222,734

Merkle Root

5be2e6f05835993eb3e6d60f3853e70e184fdcee3436a46d478c10b8b718f062
Transactions (1)
Coinbase5be2e6f0583599…8c10b8b718f062
1 in β†’ 1 out7.9300 XPM109 B
AP7WnbML…GADuS9ve
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.

9.769 Γ— 10⁹⁡(96-digit number)
97692633539299368720…07543479714584327680
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
9.769 Γ— 10⁹⁡(96-digit number)
97692633539299368720…07543479714584327679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.953 Γ— 10⁹⁢(97-digit number)
19538526707859873744…15086959429168655359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.907 Γ— 10⁹⁢(97-digit number)
39077053415719747488…30173918858337310719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.815 Γ— 10⁹⁢(97-digit number)
78154106831439494976…60347837716674621439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.563 Γ— 10⁹⁷(98-digit number)
15630821366287898995…20695675433349242879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.126 Γ— 10⁹⁷(98-digit number)
31261642732575797990…41391350866698485759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.252 Γ— 10⁹⁷(98-digit number)
62523285465151595981…82782701733396971519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.250 Γ— 10⁹⁸(99-digit number)
12504657093030319196…65565403466793943039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.500 Γ— 10⁹⁸(99-digit number)
25009314186060638392…31130806933587886079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.001 Γ— 10⁹⁸(99-digit number)
50018628372121276784…62261613867175772159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.000 Γ— 10⁹⁹(100-digit number)
10003725674424255356…24523227734351544319
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2610766

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 d24adc41a3d92af75a02f7ca2599c5eb3f493f21373733db6e5c21bf3d7a3767

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 #2,610,766 on Chainz β†—
Circulating Supply:57,912,205 XPMΒ·at block #6,833,499 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