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Home/Chain Registry/Block #2,544,083

Block #2,544,083

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/1/2018, 2:58:07 PM Β· Difficulty 10.9877 Β· 4,282,816 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
15dfc65d5207be033048849f0271509216ac31c283ade1bb9315ca1f1ad45eaa
View on Chainz β†—

Difficulty

10.987676

Transactions

1

Size

200 B

Version

2

Bits

0afcd851

Nonce

897,245,996

Timestamp

3/1/2018, 2:58:07 PM

Confirmations

4,282,816

Merkle Root

e65c03efbb67503ef9056083db98f51a756110eb29e3437ce1247ccaf684082b
Transactions (1)
Coinbasee65c03efbb6750…247ccaf684082b
1 in β†’ 1 out8.2700 XPM110 B
ATTMUYMm…TE8GxXjw
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.

7.763 Γ— 10⁹³(94-digit number)
77638556095354523425…37580402836097615360
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
7.763 Γ— 10⁹³(94-digit number)
77638556095354523425…37580402836097615361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.552 Γ— 10⁹⁴(95-digit number)
15527711219070904685…75160805672195230721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.105 Γ— 10⁹⁴(95-digit number)
31055422438141809370…50321611344390461441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.211 Γ— 10⁹⁴(95-digit number)
62110844876283618740…00643222688780922881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.242 Γ— 10⁹⁡(96-digit number)
12422168975256723748…01286445377561845761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.484 Γ— 10⁹⁡(96-digit number)
24844337950513447496…02572890755123691521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.968 Γ— 10⁹⁡(96-digit number)
49688675901026894992…05145781510247383041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.937 Γ— 10⁹⁡(96-digit number)
99377351802053789984…10291563020494766081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.987 Γ— 10⁹⁢(97-digit number)
19875470360410757996…20583126040989532161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.975 Γ— 10⁹⁢(97-digit number)
39750940720821515993…41166252081979064321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.950 Γ— 10⁹⁢(97-digit number)
79501881441643031987…82332504163958128641
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 2544083

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 15dfc65d5207be033048849f0271509216ac31c283ade1bb9315ca1f1ad45eaa

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 #2,544,083 on Chainz β†—
Circulating Supply:57,859,358 XPMΒ·at block #6,826,898 Β· updates every 60s
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