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Home/Chain Registry/Block #2,532,869

Block #2,532,869

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/22/2018, 4:43:46 AM Β· Difficulty 10.9860 Β· 4,310,094 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0a7abf87e76c8e94dd234f95e27539b3f219df5656716f303b739a21fc67f894
View on Chainz β†—

Difficulty

10.985983

Transactions

1

Size

201 B

Version

2

Bits

0afc6961

Nonce

642,214,707

Timestamp

2/22/2018, 4:43:46 AM

Confirmations

4,310,094

Merkle Root

c4a7a7a3f0bae86441eb330249b3128d75ed807f756b07f5cf13488982be7875
Transactions (1)
Coinbasec4a7a7a3f0bae8…13488982be7875
1 in β†’ 1 out8.2700 XPM110 B
AaZ8MvJn…WyNSk4cy
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.

7.421 Γ— 10⁹⁢(97-digit number)
74214039760274948652…90953408982506393600
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
7.421 Γ— 10⁹⁢(97-digit number)
74214039760274948652…90953408982506393601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.484 Γ— 10⁹⁷(98-digit number)
14842807952054989730…81906817965012787201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.968 Γ— 10⁹⁷(98-digit number)
29685615904109979461…63813635930025574401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.937 Γ— 10⁹⁷(98-digit number)
59371231808219958922…27627271860051148801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.187 Γ— 10⁹⁸(99-digit number)
11874246361643991784…55254543720102297601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.374 Γ— 10⁹⁸(99-digit number)
23748492723287983568…10509087440204595201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.749 Γ— 10⁹⁸(99-digit number)
47496985446575967137…21018174880409190401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.499 Γ— 10⁹⁸(99-digit number)
94993970893151934275…42036349760818380801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.899 Γ— 10⁹⁹(100-digit number)
18998794178630386855…84072699521636761601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.799 Γ— 10⁹⁹(100-digit number)
37997588357260773710…68145399043273523201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2532869

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 0a7abf87e76c8e94dd234f95e27539b3f219df5656716f303b739a21fc67f894

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 #2,532,869 on Chainz β†—
Circulating Supply:57,988,058 XPMΒ·at block #6,842,962 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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