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Home/Chain Registry/Block #2,824,132

Block #2,824,132

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/4/2018, 9:01:29 AM Β· Difficulty 11.7082 Β· 4,020,575 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
25fbddacd5b67e5f63c8948051e3b257e8cf12aeb1152c6de0d19bd6385cf6f9
View on Chainz β†—

Difficulty

11.708217

Transactions

1

Size

200 B

Version

2

Bits

0bb54daf

Nonce

24,808,286

Timestamp

9/4/2018, 9:01:29 AM

Confirmations

4,020,575

Merkle Root

2dd3eaa74a5c0648cb750b82a29cf26ab2fe0686175af74e24da4e1e79d3212a
Transactions (1)
Coinbase2dd3eaa74a5c06…da4e1e79d3212a
1 in β†’ 1 out7.2800 XPM110 B
AZtxQr2F…7grUWrUz
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.

5.977 Γ— 10⁹³(94-digit number)
59775149236415081068…28169332369864768320
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
5.977 Γ— 10⁹³(94-digit number)
59775149236415081068…28169332369864768319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.195 Γ— 10⁹⁴(95-digit number)
11955029847283016213…56338664739729536639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.391 Γ— 10⁹⁴(95-digit number)
23910059694566032427…12677329479459073279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.782 Γ— 10⁹⁴(95-digit number)
47820119389132064855…25354658958918146559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.564 Γ— 10⁹⁴(95-digit number)
95640238778264129710…50709317917836293119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.912 Γ— 10⁹⁡(96-digit number)
19128047755652825942…01418635835672586239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.825 Γ— 10⁹⁡(96-digit number)
38256095511305651884…02837271671345172479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.651 Γ— 10⁹⁡(96-digit number)
76512191022611303768…05674543342690344959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.530 Γ— 10⁹⁢(97-digit number)
15302438204522260753…11349086685380689919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.060 Γ— 10⁹⁢(97-digit number)
30604876409044521507…22698173370761379839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.120 Γ— 10⁹⁢(97-digit number)
61209752818089043014…45396346741522759679
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 2824132

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 25fbddacd5b67e5f63c8948051e3b257e8cf12aeb1152c6de0d19bd6385cf6f9

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 #2,824,132 on Chainz β†—
Circulating Supply:58,002,066 XPMΒ·at block #6,844,706 Β· updates every 60s
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