XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,566,679

Block #2,566,679

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/15/2018, 7:03:33 AM Β· Difficulty 10.9936 Β· 4,278,663 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
016a20c616413f3b79ec10482b965dbd5914bce07910269e5ec6e36dd2c9dfe8
View on Chainz β†—

Difficulty

10.993583

Transactions

1

Size

198 B

Version

2

Bits

0afe5b6f

Nonce

455,299,728

Timestamp

3/15/2018, 7:03:33 AM

Confirmations

4,278,663

Merkle Root

2173db0cbe94f923e4f2024d213ed2d6e046ccee0bbb1e3a3e2ffdcc34b1bc22
Transactions (1)
Coinbase2173db0cbe94f9…2ffdcc34b1bc22
1 in β†’ 1 out8.2600 XPM109 B
AKCMfqTQ…oKkCRKgX
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.

3.277 Γ— 10⁹²(93-digit number)
32775689009214796582…53944508031048638080
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
3.277 Γ— 10⁹²(93-digit number)
32775689009214796582…53944508031048638081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.555 Γ— 10⁹²(93-digit number)
65551378018429593165…07889016062097276161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.311 Γ— 10⁹³(94-digit number)
13110275603685918633…15778032124194552321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.622 Γ— 10⁹³(94-digit number)
26220551207371837266…31556064248389104641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.244 Γ— 10⁹³(94-digit number)
52441102414743674532…63112128496778209281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.048 Γ— 10⁹⁴(95-digit number)
10488220482948734906…26224256993556418561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.097 Γ— 10⁹⁴(95-digit number)
20976440965897469812…52448513987112837121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.195 Γ— 10⁹⁴(95-digit number)
41952881931794939625…04897027974225674241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.390 Γ— 10⁹⁴(95-digit number)
83905763863589879251…09794055948451348481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.678 Γ— 10⁹⁡(96-digit number)
16781152772717975850…19588111896902696961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.356 Γ— 10⁹⁡(96-digit number)
33562305545435951700…39176223793805393921
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 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
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 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 2566679

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 016a20c616413f3b79ec10482b965dbd5914bce07910269e5ec6e36dd2c9dfe8

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 #2,566,679 on Chainz β†—
Circulating Supply:58,007,177 XPMΒ·at block #6,845,341 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