XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,558,639

Block #2,558,639

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/10/2018, 12:00:05 PM Β· Difficulty 10.9917 Β· 4,274,559 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b28c9bbedc2d62a1e17ff65616987d798b636d1c372c680cd393cfe2dc884357
View on Chainz β†—

Difficulty

10.991690

Transactions

1

Size

200 B

Version

2

Bits

0afddf6b

Nonce

764,662,972

Timestamp

3/10/2018, 12:00:05 PM

Confirmations

4,274,559

Merkle Root

bff4e6dea9be56071ed4bc326a437e18f00a6d630d3857b132ded221f10b3e7a
Transactions (1)
Coinbasebff4e6dea9be56…ded221f10b3e7a
1 in β†’ 1 out8.2600 XPM110 B
Ad21tJiC…hi6ZDXmC
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.

1.199 Γ— 10⁹⁡(96-digit number)
11994745530168902620…36170939134453197440
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
1.199 Γ— 10⁹⁡(96-digit number)
11994745530168902620…36170939134453197441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.398 Γ— 10⁹⁡(96-digit number)
23989491060337805241…72341878268906394881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.797 Γ— 10⁹⁡(96-digit number)
47978982120675610482…44683756537812789761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.595 Γ— 10⁹⁡(96-digit number)
95957964241351220964…89367513075625579521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.919 Γ— 10⁹⁢(97-digit number)
19191592848270244192…78735026151251159041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.838 Γ— 10⁹⁢(97-digit number)
38383185696540488385…57470052302502318081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.676 Γ— 10⁹⁢(97-digit number)
76766371393080976771…14940104605004636161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.535 Γ— 10⁹⁷(98-digit number)
15353274278616195354…29880209210009272321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.070 Γ— 10⁹⁷(98-digit number)
30706548557232390708…59760418420018544641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.141 Γ— 10⁹⁷(98-digit number)
61413097114464781417…19520836840037089281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.228 Γ— 10⁹⁸(99-digit number)
12282619422892956283…39041673680074178561
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 2558639

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 b28c9bbedc2d62a1e17ff65616987d798b636d1c372c680cd393cfe2dc884357

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 #2,558,639 on Chainz β†—
Circulating Supply:57,909,770 XPMΒ·at block #6,833,197 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