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Block #288,424

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/1/2013, 5:54:35 PM Β· Difficulty 9.9877 Β· 6,538,283 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7c095da797ee770b2279ae57ea1c4bc780bfe2cf34ea0160443a6a0e465e8b22
View on Chainz β†—

Height

#288,424

Difficulty

9.987690

Transactions

1

Size

206 B

Version

2

Bits

09fcd940

Nonce

190,571

Timestamp

12/1/2013, 5:54:35 PM

Confirmations

6,538,283

Merkle Root

aebfae423955f495f2fd24151c72a0a9f31de3a78353deed521a5fcffecf60c4
Transactions (1)
Coinbaseaebfae423955f4…1a5fcffecf60c4
1 in β†’ 1 out10.0100 XPM116 B
AcLBm5Z9…S683d7c3
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.

4.364 Γ— 10⁹⁴(95-digit number)
43641181462276866035…23156636034239691480
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
4.364 Γ— 10⁹⁴(95-digit number)
43641181462276866035…23156636034239691481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.728 Γ— 10⁹⁴(95-digit number)
87282362924553732070…46313272068479382961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.745 Γ— 10⁹⁡(96-digit number)
17456472584910746414…92626544136958765921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.491 Γ— 10⁹⁡(96-digit number)
34912945169821492828…85253088273917531841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.982 Γ— 10⁹⁡(96-digit number)
69825890339642985656…70506176547835063681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.396 Γ— 10⁹⁢(97-digit number)
13965178067928597131…41012353095670127361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.793 Γ— 10⁹⁢(97-digit number)
27930356135857194262…82024706191340254721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.586 Γ— 10⁹⁢(97-digit number)
55860712271714388525…64049412382680509441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.117 Γ— 10⁹⁷(98-digit number)
11172142454342877705…28098824765361018881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.234 Γ— 10⁹⁷(98-digit number)
22344284908685755410…56197649530722037761
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 288424

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 7c095da797ee770b2279ae57ea1c4bc780bfe2cf34ea0160443a6a0e465e8b22

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 #288,424 on Chainz β†—
Circulating Supply:57,857,808 XPMΒ·at block #6,826,706 Β· updates every 60s
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