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Home/Chain Registry/Block #2,611,563

Block #2,611,563

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/13/2018, 3:41:02 AM Β· Difficulty 11.2144 Β· 4,233,178 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
db3ba212725b4a1377b91663572f32627890cdff23966dc285df24737250ff75
View on Chainz β†—

Difficulty

11.214420

Transactions

1

Size

199 B

Version

2

Bits

0b36e43e

Nonce

1,498,939,403

Timestamp

4/13/2018, 3:41:02 AM

Confirmations

4,233,178

Merkle Root

d2769a216d58e82d99cc8b210de44f35c11b341a726ef5d5b4c3c09badd98f6c
Transactions (1)
Coinbased2769a216d58e8…c3c09badd98f6c
1 in β†’ 1 out7.9400 XPM110 B
Adqah8zh…1WwoHJ9t
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.

4.910 Γ— 10⁹²(93-digit number)
49106638778529628266…96669708014458348400
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
4.910 Γ— 10⁹²(93-digit number)
49106638778529628266…96669708014458348401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.821 Γ— 10⁹²(93-digit number)
98213277557059256532…93339416028916696801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.964 Γ— 10⁹³(94-digit number)
19642655511411851306…86678832057833393601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.928 Γ— 10⁹³(94-digit number)
39285311022823702612…73357664115666787201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.857 Γ— 10⁹³(94-digit number)
78570622045647405225…46715328231333574401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.571 Γ— 10⁹⁴(95-digit number)
15714124409129481045…93430656462667148801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.142 Γ— 10⁹⁴(95-digit number)
31428248818258962090…86861312925334297601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.285 Γ— 10⁹⁴(95-digit number)
62856497636517924180…73722625850668595201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.257 Γ— 10⁹⁡(96-digit number)
12571299527303584836…47445251701337190401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.514 Γ— 10⁹⁡(96-digit number)
25142599054607169672…94890503402674380801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.028 Γ— 10⁹⁡(96-digit number)
50285198109214339344…89781006805348761601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.005 Γ— 10⁹⁢(97-digit number)
10057039621842867868…79562013610697523201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2611563

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 db3ba212725b4a1377b91663572f32627890cdff23966dc285df24737250ff75

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 #2,611,563 on Chainz β†—
Circulating Supply:58,002,340 XPMΒ·at block #6,844,740 Β· updates every 60s
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