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Home/Chain Registry/Block #2,641,621

Block #2,641,621

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/1/2018, 10:24:02 AM Β· Difficulty 11.6261 Β· 4,189,924 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5fd8e481d708d7b0fc8b2c00f5292062d6d74bc89fd82bcbf0a97dbab87c8779
View on Chainz β†—

Difficulty

11.626092

Transactions

1

Size

200 B

Version

2

Bits

0ba04799

Nonce

70,090,208

Timestamp

5/1/2018, 10:24:02 AM

Confirmations

4,189,924

Merkle Root

68f337753d9d3f2d48daf9acb416dda51b2e0200a275a03b2b36c070ba90b6d8
Transactions (1)
Coinbase68f337753d9d3f…36c070ba90b6d8
1 in β†’ 1 out7.3900 XPM110 B
AFp8BxLZ…KVCQBYsP
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.

1.386 Γ— 10⁹⁴(95-digit number)
13868233944677029628…42143198502614858510
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
1.386 Γ— 10⁹⁴(95-digit number)
13868233944677029628…42143198502614858509
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.773 Γ— 10⁹⁴(95-digit number)
27736467889354059256…84286397005229717019
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.547 Γ— 10⁹⁴(95-digit number)
55472935778708118512…68572794010459434039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.109 Γ— 10⁹⁡(96-digit number)
11094587155741623702…37145588020918868079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.218 Γ— 10⁹⁡(96-digit number)
22189174311483247404…74291176041837736159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.437 Γ— 10⁹⁡(96-digit number)
44378348622966494809…48582352083675472319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.875 Γ— 10⁹⁡(96-digit number)
88756697245932989619…97164704167350944639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.775 Γ— 10⁹⁢(97-digit number)
17751339449186597923…94329408334701889279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.550 Γ— 10⁹⁢(97-digit number)
35502678898373195847…88658816669403778559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.100 Γ— 10⁹⁢(97-digit number)
71005357796746391695…77317633338807557119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.420 Γ— 10⁹⁷(98-digit number)
14201071559349278339…54635266677615114239
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 2641621

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 5fd8e481d708d7b0fc8b2c00f5292062d6d74bc89fd82bcbf0a97dbab87c8779

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 #2,641,621 on Chainz β†—
Circulating Supply:57,896,450 XPMΒ·at block #6,831,544 Β· updates every 60s
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