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Home/Chain Registry/Block #2,650,496

Block #2,650,496

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/6/2018, 2:19:44 AM Β· Difficulty 11.7567 Β· 4,195,153 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cb8c13081cb212a7a1931eb0e3132e8b1aa2786e817e50c182ad33c97a7bd36c
View on Chainz β†—

Difficulty

11.756729

Transactions

1

Size

200 B

Version

2

Bits

0bc1b8fa

Nonce

1,587,901,771

Timestamp

5/6/2018, 2:19:44 AM

Confirmations

4,195,153

Merkle Root

2bbcbec923ee2981dde056430c77f9ecddcd50e51eba6dff2d211963fe20b784
Transactions (1)
Coinbase2bbcbec923ee29…211963fe20b784
1 in β†’ 1 out7.2200 XPM110 B
AZAmrKGq…BNie63Qq
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.

3.081 Γ— 10⁹⁡(96-digit number)
30817346908077107041…67827312295988630320
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
3.081 Γ— 10⁹⁡(96-digit number)
30817346908077107041…67827312295988630321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.163 Γ— 10⁹⁡(96-digit number)
61634693816154214082…35654624591977260641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.232 Γ— 10⁹⁢(97-digit number)
12326938763230842816…71309249183954521281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.465 Γ— 10⁹⁢(97-digit number)
24653877526461685632…42618498367909042561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.930 Γ— 10⁹⁢(97-digit number)
49307755052923371265…85236996735818085121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.861 Γ— 10⁹⁢(97-digit number)
98615510105846742531…70473993471636170241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.972 Γ— 10⁹⁷(98-digit number)
19723102021169348506…40947986943272340481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.944 Γ— 10⁹⁷(98-digit number)
39446204042338697012…81895973886544680961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.889 Γ— 10⁹⁷(98-digit number)
78892408084677394025…63791947773089361921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.577 Γ— 10⁹⁸(99-digit number)
15778481616935478805…27583895546178723841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.155 Γ— 10⁹⁸(99-digit number)
31556963233870957610…55167791092357447681
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 2650496

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 cb8c13081cb212a7a1931eb0e3132e8b1aa2786e817e50c182ad33c97a7bd36c

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 #2,650,496 on Chainz β†—
Circulating Supply:58,009,641 XPMΒ·at block #6,845,648 Β· updates every 60s
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