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Home/Chain Registry/Block #2,469,288

Block #2,469,288

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/12/2018, 10:20:42 AM Β· Difficulty 10.9600 Β· 4,373,190 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cec2fba21dddf8d1489be74cc43e7bde8ee1b94f3f4c5eb2840acd3c4e70997e
View on Chainz β†—

Difficulty

10.959989

Transactions

1

Size

199 B

Version

2

Bits

0af5c1d0

Nonce

329,975,659

Timestamp

1/12/2018, 10:20:42 AM

Confirmations

4,373,190

Merkle Root

e9bc7183c8e8af4362bf1d09bd39730a5e99ab5c56291e76a5a0cd906cf0b928
Transactions (1)
Coinbasee9bc7183c8e8af…a0cd906cf0b928
1 in β†’ 1 out8.3100 XPM110 B
AJKLRq6r…SKM6NSvV
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.

1.246 Γ— 10⁹²(93-digit number)
12465780023212100455…13954434270718852160
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
1.246 Γ— 10⁹²(93-digit number)
12465780023212100455…13954434270718852161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.493 Γ— 10⁹²(93-digit number)
24931560046424200910…27908868541437704321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.986 Γ— 10⁹²(93-digit number)
49863120092848401820…55817737082875408641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.972 Γ— 10⁹²(93-digit number)
99726240185696803641…11635474165750817281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.994 Γ— 10⁹³(94-digit number)
19945248037139360728…23270948331501634561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.989 Γ— 10⁹³(94-digit number)
39890496074278721456…46541896663003269121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.978 Γ— 10⁹³(94-digit number)
79780992148557442913…93083793326006538241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.595 Γ— 10⁹⁴(95-digit number)
15956198429711488582…86167586652013076481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.191 Γ— 10⁹⁴(95-digit number)
31912396859422977165…72335173304026152961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.382 Γ— 10⁹⁴(95-digit number)
63824793718845954330…44670346608052305921
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 2469288

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 cec2fba21dddf8d1489be74cc43e7bde8ee1b94f3f4c5eb2840acd3c4e70997e

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 #2,469,288 on Chainz β†—
Circulating Supply:57,984,241 XPMΒ·at block #6,842,477 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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