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Home/Chain Registry/Block #2,790,601

Block #2,790,601

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/12/2018, 10:59:55 AM Β· Difficulty 11.6748 Β· 4,010,960 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7f7e64aa4c09a1411cb6a13a8d49c0cd1c5338ee3ce91f62ffc53bf75c5b01f7
View on Chainz β†—

Difficulty

11.674764

Transactions

1

Size

201 B

Version

2

Bits

0bacbd58

Nonce

925,300,380

Timestamp

8/12/2018, 10:59:55 AM

Confirmations

4,010,960

Merkle Root

f6042d566de1fc2a63228faab8b8073e97ae1933d34e8728458349041548584d
Transactions (1)
Coinbasef6042d566de1fc…8349041548584d
1 in β†’ 1 out7.3200 XPM110 B
AVoaMjaQ…21k3For2
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.

3.332 Γ— 10⁹⁷(98-digit number)
33324022042904736482…12525530855050485760
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
3.332 Γ— 10⁹⁷(98-digit number)
33324022042904736482…12525530855050485761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.664 Γ— 10⁹⁷(98-digit number)
66648044085809472965…25051061710100971521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.332 Γ— 10⁹⁸(99-digit number)
13329608817161894593…50102123420201943041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.665 Γ— 10⁹⁸(99-digit number)
26659217634323789186…00204246840403886081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.331 Γ— 10⁹⁸(99-digit number)
53318435268647578372…00408493680807772161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.066 Γ— 10⁹⁹(100-digit number)
10663687053729515674…00816987361615544321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.132 Γ— 10⁹⁹(100-digit number)
21327374107459031348…01633974723231088641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.265 Γ— 10⁹⁹(100-digit number)
42654748214918062697…03267949446462177281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.530 Γ— 10⁹⁹(100-digit number)
85309496429836125395…06535898892924354561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.706 Γ— 10¹⁰⁰(101-digit number)
17061899285967225079…13071797785848709121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.412 Γ— 10¹⁰⁰(101-digit number)
34123798571934450158…26143595571697418241
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 2790601

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 7f7e64aa4c09a1411cb6a13a8d49c0cd1c5338ee3ce91f62ffc53bf75c5b01f7

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 #2,790,601 on Chainz β†—
Circulating Supply:57,656,569 XPMΒ·at block #6,801,560 Β· updates every 60s
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