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Home/Chain Registry/Block #2,641,935

Block #2,641,935

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/1/2018, 1:08:32 PM Β· Difficulty 11.6371 Β· 4,199,466 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
eea899b0335bde6888ea0c57b2a39af3228457e8af8a9a1d5a91b498bb6cd605
View on Chainz β†—

Difficulty

11.637082

Transactions

1

Size

200 B

Version

2

Bits

0ba317c7

Nonce

96,511,350

Timestamp

5/1/2018, 1:08:32 PM

Confirmations

4,199,466

Merkle Root

7379d7f077dede960d0877828f37f06eb890d7e6b9ce23cba1313d4535566afd
Transactions (1)
Coinbase7379d7f077dede…313d4535566afd
1 in β†’ 1 out7.3700 XPM110 B
AFvhDK5b…4RyfSi2s
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.

6.798 Γ— 10⁹⁴(95-digit number)
67989598348991882321…33205509845139324360
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
6.798 Γ— 10⁹⁴(95-digit number)
67989598348991882321…33205509845139324359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.359 Γ— 10⁹⁡(96-digit number)
13597919669798376464…66411019690278648719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.719 Γ— 10⁹⁡(96-digit number)
27195839339596752928…32822039380557297439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.439 Γ— 10⁹⁡(96-digit number)
54391678679193505857…65644078761114594879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.087 Γ— 10⁹⁢(97-digit number)
10878335735838701171…31288157522229189759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.175 Γ— 10⁹⁢(97-digit number)
21756671471677402342…62576315044458379519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.351 Γ— 10⁹⁢(97-digit number)
43513342943354804685…25152630088916759039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.702 Γ— 10⁹⁢(97-digit number)
87026685886709609371…50305260177833518079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.740 Γ— 10⁹⁷(98-digit number)
17405337177341921874…00610520355667036159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.481 Γ— 10⁹⁷(98-digit number)
34810674354683843748…01221040711334072319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.962 Γ— 10⁹⁷(98-digit number)
69621348709367687496…02442081422668144639
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 2641935

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 eea899b0335bde6888ea0c57b2a39af3228457e8af8a9a1d5a91b498bb6cd605

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 #2,641,935 on Chainz β†—
Circulating Supply:57,975,581 XPMΒ·at block #6,841,400 Β· updates every 60s
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