XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,687,264

Block #2,687,264

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/1/2018, 2:11:22 PM Β· Difficulty 11.6812 Β· 4,156,834 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
068febff03af836088aa6fd36abcecb4ee8e36ed6c2478b04d85e686fba55f2f
View on Chainz β†—

Difficulty

11.681230

Transactions

1

Size

200 B

Version

2

Bits

0bae6510

Nonce

892,604,019

Timestamp

6/1/2018, 2:11:22 PM

Confirmations

4,156,834

Merkle Root

b8b362a499530876cad6eb6078f0ddcce532189a7a43a5bd1450057cf94974be
Transactions (1)
Coinbaseb8b362a4995308…50057cf94974be
1 in β†’ 1 out7.3200 XPM110 B
AJnGSjhJ…DPNGyUm4
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.

1.580 Γ— 10⁹⁴(95-digit number)
15802291400160511714…13214400373600929920
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
1.580 Γ— 10⁹⁴(95-digit number)
15802291400160511714…13214400373600929919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.160 Γ— 10⁹⁴(95-digit number)
31604582800321023429…26428800747201859839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.320 Γ— 10⁹⁴(95-digit number)
63209165600642046858…52857601494403719679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.264 Γ— 10⁹⁡(96-digit number)
12641833120128409371…05715202988807439359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.528 Γ— 10⁹⁡(96-digit number)
25283666240256818743…11430405977614878719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.056 Γ— 10⁹⁡(96-digit number)
50567332480513637486…22860811955229757439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.011 Γ— 10⁹⁢(97-digit number)
10113466496102727497…45721623910459514879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.022 Γ— 10⁹⁢(97-digit number)
20226932992205454994…91443247820919029759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.045 Γ— 10⁹⁢(97-digit number)
40453865984410909989…82886495641838059519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.090 Γ— 10⁹⁢(97-digit number)
80907731968821819979…65772991283676119039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.618 Γ— 10⁹⁷(98-digit number)
16181546393764363995…31545982567352238079
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 2687264

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 068febff03af836088aa6fd36abcecb4ee8e36ed6c2478b04d85e686fba55f2f

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 #2,687,264 on Chainz β†—
Circulating Supply:57,997,157 XPMΒ·at block #6,844,097 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