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Home/Chain Registry/Block #2,495,228

Block #2,495,228

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/29/2018, 2:01:21 AM Β· Difficulty 10.9735 Β· 4,349,276 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ba704baf52293dcc506baa25ca743bb3a6a5d7c962c5a14fa851e18873be859d
View on Chainz β†—

Difficulty

10.973507

Transactions

1

Size

201 B

Version

2

Bits

0af937bd

Nonce

1,116,845,705

Timestamp

1/29/2018, 2:01:21 AM

Confirmations

4,349,276

Merkle Root

d150afce2a4bf5bd2f5c6b53d685cd85fdb763396c9540871250192077210b40
Transactions (1)
Coinbased150afce2a4bf5…50192077210b40
1 in β†’ 1 out8.2900 XPM110 B
AKyDGaqh…pseg38wo
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.

3.991 Γ— 10⁹⁢(97-digit number)
39911397719237902533…88555449755075627520
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
3.991 Γ— 10⁹⁢(97-digit number)
39911397719237902533…88555449755075627519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.982 Γ— 10⁹⁢(97-digit number)
79822795438475805066…77110899510151255039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.596 Γ— 10⁹⁷(98-digit number)
15964559087695161013…54221799020302510079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.192 Γ— 10⁹⁷(98-digit number)
31929118175390322026…08443598040605020159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.385 Γ— 10⁹⁷(98-digit number)
63858236350780644053…16887196081210040319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.277 Γ— 10⁹⁸(99-digit number)
12771647270156128810…33774392162420080639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.554 Γ— 10⁹⁸(99-digit number)
25543294540312257621…67548784324840161279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.108 Γ— 10⁹⁸(99-digit number)
51086589080624515242…35097568649680322559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.021 Γ— 10⁹⁹(100-digit number)
10217317816124903048…70195137299360645119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.043 Γ— 10⁹⁹(100-digit number)
20434635632249806097…40390274598721290239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.086 Γ— 10⁹⁹(100-digit number)
40869271264499612194…80780549197442580479
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 2495228

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 ba704baf52293dcc506baa25ca743bb3a6a5d7c962c5a14fa851e18873be859d

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 #2,495,228 on Chainz β†—
Circulating Supply:58,000,430 XPMΒ·at block #6,844,503 Β· updates every 60s
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