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Home/Chain Registry/Block #2,633,813

Block #2,633,813

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/28/2018, 3:08:31 PM Β· Difficulty 11.2093 Β· 4,209,301 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fba1e8e690d6dd6ef2af41126ca48ef3df1b46f295deaa5b31d43f205c8838ba
View on Chainz β†—

Difficulty

11.209317

Transactions

1

Size

201 B

Version

2

Bits

0b3595d1

Nonce

2,088,704,353

Timestamp

4/28/2018, 3:08:31 PM

Confirmations

4,209,301

Merkle Root

6c7c566d7fc47a2e0cb16657cc90e5669416a962b6eee5774068a17b3ae2cb2a
Transactions (1)
Coinbase6c7c566d7fc47a…68a17b3ae2cb2a
1 in β†’ 1 out7.9500 XPM110 B
ARJrDun3…MjrTDwrV
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.

5.060 Γ— 10⁹⁢(97-digit number)
50609094222433896484…34940730681364222080
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
5.060 Γ— 10⁹⁢(97-digit number)
50609094222433896484…34940730681364222079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.012 Γ— 10⁹⁷(98-digit number)
10121818844486779296…69881461362728444159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.024 Γ— 10⁹⁷(98-digit number)
20243637688973558593…39762922725456888319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.048 Γ— 10⁹⁷(98-digit number)
40487275377947117187…79525845450913776639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.097 Γ— 10⁹⁷(98-digit number)
80974550755894234375…59051690901827553279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.619 Γ— 10⁹⁸(99-digit number)
16194910151178846875…18103381803655106559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.238 Γ— 10⁹⁸(99-digit number)
32389820302357693750…36206763607310213119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.477 Γ— 10⁹⁸(99-digit number)
64779640604715387500…72413527214620426239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.295 Γ— 10⁹⁹(100-digit number)
12955928120943077500…44827054429240852479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.591 Γ— 10⁹⁹(100-digit number)
25911856241886155000…89654108858481704959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.182 Γ— 10⁹⁹(100-digit number)
51823712483772310000…79308217716963409919
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 2633813

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 fba1e8e690d6dd6ef2af41126ca48ef3df1b46f295deaa5b31d43f205c8838ba

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 #2,633,813 on Chainz β†—
Circulating Supply:57,989,277 XPMΒ·at block #6,843,113 Β· updates every 60s
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