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Home/Chain Registry/Block #2,274,717

Block #2,274,717

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/30/2017, 10:39:08 AM Β· Difficulty 10.9549 Β· 4,562,127 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9602cbd8b3f053c4d942be515ca18f6842d987e53ce0a24934adafa908070bf0
View on Chainz β†—

Difficulty

10.954942

Transactions

1

Size

201 B

Version

2

Bits

0af47715

Nonce

866,622,021

Timestamp

8/30/2017, 10:39:08 AM

Confirmations

4,562,127

Merkle Root

8f0da337f2af511b305d09dc71dd5fb8c205cfb91ff4f1fed2762a88de5ad152
Transactions (1)
Coinbase8f0da337f2af51…762a88de5ad152
1 in β†’ 1 out8.3200 XPM110 B
AVxmhbWp…9kSr6foS
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.

1.631 Γ— 10⁹⁢(97-digit number)
16313390531414261044…56930600280309985280
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.631 Γ— 10⁹⁢(97-digit number)
16313390531414261044…56930600280309985279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.262 Γ— 10⁹⁢(97-digit number)
32626781062828522089…13861200560619970559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.525 Γ— 10⁹⁢(97-digit number)
65253562125657044178…27722401121239941119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.305 Γ— 10⁹⁷(98-digit number)
13050712425131408835…55444802242479882239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.610 Γ— 10⁹⁷(98-digit number)
26101424850262817671…10889604484959764479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.220 Γ— 10⁹⁷(98-digit number)
52202849700525635343…21779208969919528959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.044 Γ— 10⁹⁸(99-digit number)
10440569940105127068…43558417939839057919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.088 Γ— 10⁹⁸(99-digit number)
20881139880210254137…87116835879678115839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.176 Γ— 10⁹⁸(99-digit number)
41762279760420508274…74233671759356231679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.352 Γ— 10⁹⁸(99-digit number)
83524559520841016549…48467343518712463359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.670 Γ— 10⁹⁹(100-digit number)
16704911904168203309…96934687037424926719
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2274717

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 9602cbd8b3f053c4d942be515ca18f6842d987e53ce0a24934adafa908070bf0

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 #2,274,717 on Chainz β†—
Circulating Supply:57,939,040 XPMΒ·at block #6,836,843 Β· updates every 60s
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