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Home/Chain Registry/Block #2,752,880

Block #2,752,880

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/17/2018, 11:39:25 AM Β· Difficulty 11.6520 Β· 4,090,307 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
369e950abca5c0af91708c1e9fba006a43bf81e97ff41d0b145ec607cc00364d
View on Chainz β†—

Difficulty

11.651984

Transactions

1

Size

201 B

Version

2

Bits

0ba6e86c

Nonce

1,895,975,866

Timestamp

7/17/2018, 11:39:25 AM

Confirmations

4,090,307

Merkle Root

9834087e0daf7f71827a5e5f13343d5bd1d8dfe12fd3e4f46a934113d1270342
Transactions (1)
Coinbase9834087e0daf7f…934113d1270342
1 in β†’ 1 out7.3500 XPM110 B
AV6MREa8…r3SrPza5
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.

2.135 Γ— 10⁹⁷(98-digit number)
21356619050683933013…79620347578812695040
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
2.135 Γ— 10⁹⁷(98-digit number)
21356619050683933013…79620347578812695039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.271 Γ— 10⁹⁷(98-digit number)
42713238101367866027…59240695157625390079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.542 Γ— 10⁹⁷(98-digit number)
85426476202735732055…18481390315250780159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.708 Γ— 10⁹⁸(99-digit number)
17085295240547146411…36962780630501560319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.417 Γ— 10⁹⁸(99-digit number)
34170590481094292822…73925561261003120639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.834 Γ— 10⁹⁸(99-digit number)
68341180962188585644…47851122522006241279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.366 Γ— 10⁹⁹(100-digit number)
13668236192437717128…95702245044012482559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.733 Γ— 10⁹⁹(100-digit number)
27336472384875434257…91404490088024965119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.467 Γ— 10⁹⁹(100-digit number)
54672944769750868515…82808980176049930239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.093 Γ— 10¹⁰⁰(101-digit number)
10934588953950173703…65617960352099860479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.186 Γ— 10¹⁰⁰(101-digit number)
21869177907900347406…31235920704199720959
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 2752880

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 369e950abca5c0af91708c1e9fba006a43bf81e97ff41d0b145ec607cc00364d

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 #2,752,880 on Chainz β†—
Circulating Supply:57,989,864 XPMΒ·at block #6,843,186 Β· updates every 60s
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