XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,644,116

Block #2,644,116

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2018, 8:51:34 AM Β· Difficulty 11.7023 Β· 4,196,123 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5fc4ccbe6f2fbbce7b015107efe52e39af04555f96e6e926c78a62199553faf2
View on Chainz β†—

Difficulty

11.702305

Transactions

1

Size

200 B

Version

2

Bits

0bb3ca47

Nonce

273,775,476

Timestamp

5/2/2018, 8:51:34 AM

Confirmations

4,196,123

Merkle Root

4a20595dcc16ff736257748a59d5b4cd9e1f32b09dfe429471e299c15ffadf01
Transactions (1)
Coinbase4a20595dcc16ff…e299c15ffadf01
1 in β†’ 1 out7.2900 XPM110 B
ATvWWJmP…4h4hQ51F
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.

2.150 Γ— 10⁹⁴(95-digit number)
21502521387003188354…30311088007898293440
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
2.150 Γ— 10⁹⁴(95-digit number)
21502521387003188354…30311088007898293439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.300 Γ— 10⁹⁴(95-digit number)
43005042774006376709…60622176015796586879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.601 Γ— 10⁹⁴(95-digit number)
86010085548012753419…21244352031593173759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.720 Γ— 10⁹⁡(96-digit number)
17202017109602550683…42488704063186347519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.440 Γ— 10⁹⁡(96-digit number)
34404034219205101367…84977408126372695039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.880 Γ— 10⁹⁡(96-digit number)
68808068438410202735…69954816252745390079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.376 Γ— 10⁹⁢(97-digit number)
13761613687682040547…39909632505490780159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.752 Γ— 10⁹⁢(97-digit number)
27523227375364081094…79819265010981560319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.504 Γ— 10⁹⁢(97-digit number)
55046454750728162188…59638530021963120639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.100 Γ— 10⁹⁷(98-digit number)
11009290950145632437…19277060043926241279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.201 Γ— 10⁹⁷(98-digit number)
22018581900291264875…38554120087852482559
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 2644116

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 5fc4ccbe6f2fbbce7b015107efe52e39af04555f96e6e926c78a62199553faf2

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 #2,644,116 on Chainz β†—
Circulating Supply:57,966,224 XPMΒ·at block #6,840,238 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