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Home/Chain Registry/Block #2,641,332

Block #2,641,332

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 7:45:25 AM Β· Difficulty 11.6164 Β· 4,203,791 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6f19793db1f4a35434d14fb39cf674310dd840d73f82b5bb73f6d070761fa713
View on Chainz β†—

Difficulty

11.616370

Transactions

2

Size

2.00 KB

Version

2

Bits

0b9dca74

Nonce

72,018,199

Timestamp

5/1/2018, 7:45:25 AM

Confirmations

4,203,791

Merkle Root

42319bd9322fb1a626aa36b48c073ff6f7a0146e13e5df5df59f63bd76409f11
Transactions (2)
Coinbasee35d91a41a9a09…f484ece34ab36f
1 in β†’ 1 out7.4300 XPM110 B
APdB2kQq…2VKXNvoL
a9dde3bf20970d…d5145aa45a897a
12 in β†’ 2 out10000.0100 XPM1.81 KB
AJZ9UNRa…9RACnr4GALPF8J52…Hjw4BMsG
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.

8.907 Γ— 10⁹⁴(95-digit number)
89079535117199340426…02169213402566974400
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
8.907 Γ— 10⁹⁴(95-digit number)
89079535117199340426…02169213402566974401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.781 Γ— 10⁹⁡(96-digit number)
17815907023439868085…04338426805133948801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.563 Γ— 10⁹⁡(96-digit number)
35631814046879736170…08676853610267897601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.126 Γ— 10⁹⁡(96-digit number)
71263628093759472340…17353707220535795201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.425 Γ— 10⁹⁢(97-digit number)
14252725618751894468…34707414441071590401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.850 Γ— 10⁹⁢(97-digit number)
28505451237503788936…69414828882143180801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.701 Γ— 10⁹⁢(97-digit number)
57010902475007577872…38829657764286361601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.140 Γ— 10⁹⁷(98-digit number)
11402180495001515574…77659315528572723201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.280 Γ— 10⁹⁷(98-digit number)
22804360990003031149…55318631057145446401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.560 Γ— 10⁹⁷(98-digit number)
45608721980006062298…10637262114290892801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.121 Γ— 10⁹⁷(98-digit number)
91217443960012124596…21274524228581785601
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2641332

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 6f19793db1f4a35434d14fb39cf674310dd840d73f82b5bb73f6d070761fa713

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 #2,641,332 on Chainz β†—
Circulating Supply:58,005,412 XPMΒ·at block #6,845,122 Β· updates every 60s
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