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Home/Chain Registry/Block #2,580,269

Block #2,580,269

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/23/2018, 3:07:29 AM Β· Difficulty 11.0366 Β· 4,256,260 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
777c037bd92805339329d6ad957c59ca85b021bb99bac30449e7d4cdf119208e
View on Chainz β†—

Difficulty

11.036578

Transactions

1

Size

201 B

Version

2

Bits

0b095d30

Nonce

970,981,002

Timestamp

3/23/2018, 3:07:29 AM

Confirmations

4,256,260

Merkle Root

bacad6992a392a8968709f392030bbb28246af3bcd41961474be4bc4772279bb
Transactions (1)
Coinbasebacad6992a392a…be4bc4772279bb
1 in β†’ 1 out8.2000 XPM110 B
AL6aZuFT…AiinjCFi
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.

1.507 Γ— 10⁹⁸(99-digit number)
15070435128529549423…88273895413400780800
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
1.507 Γ— 10⁹⁸(99-digit number)
15070435128529549423…88273895413400780801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.014 Γ— 10⁹⁸(99-digit number)
30140870257059098847…76547790826801561601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.028 Γ— 10⁹⁸(99-digit number)
60281740514118197694…53095581653603123201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.205 Γ— 10⁹⁹(100-digit number)
12056348102823639538…06191163307206246401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.411 Γ— 10⁹⁹(100-digit number)
24112696205647279077…12382326614412492801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.822 Γ— 10⁹⁹(100-digit number)
48225392411294558155…24764653228824985601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.645 Γ— 10⁹⁹(100-digit number)
96450784822589116311…49529306457649971201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.929 Γ— 10¹⁰⁰(101-digit number)
19290156964517823262…99058612915299942401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.858 Γ— 10¹⁰⁰(101-digit number)
38580313929035646524…98117225830599884801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.716 Γ— 10¹⁰⁰(101-digit number)
77160627858071293049…96234451661199769601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.543 Γ— 10¹⁰¹(102-digit number)
15432125571614258609…92468903322399539201
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 2580269

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 777c037bd92805339329d6ad957c59ca85b021bb99bac30449e7d4cdf119208e

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 #2,580,269 on Chainz β†—
Circulating Supply:57,936,501 XPMΒ·at block #6,836,528 Β· updates every 60s
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