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Home/Chain Registry/Block #2,646,158

Block #2,646,158

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2018, 5:44:11 AM Β· Difficulty 11.7455 Β· 4,190,380 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e866403ad4490c613ffda743691437c2540dcf692c3d6a7cd439567d36366ee9
View on Chainz β†—

Difficulty

11.745522

Transactions

1

Size

199 B

Version

2

Bits

0bbeda86

Nonce

235,812,940

Timestamp

5/3/2018, 5:44:11 AM

Confirmations

4,190,380

Merkle Root

1c4b9aae7dc96df2d4ee0081536e234eda9528aedbcfae9407275dbaadf1eb9f
Transactions (1)
Coinbase1c4b9aae7dc96d…275dbaadf1eb9f
1 in β†’ 1 out7.2400 XPM109 B
Ae8AbEzm…Js4KqsZ9
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.

1.269 Γ— 10⁹⁡(96-digit number)
12692070755668698221…20534084988513414400
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
1.269 Γ— 10⁹⁡(96-digit number)
12692070755668698221…20534084988513414401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.538 Γ— 10⁹⁡(96-digit number)
25384141511337396442…41068169977026828801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.076 Γ— 10⁹⁡(96-digit number)
50768283022674792885…82136339954053657601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.015 Γ— 10⁹⁢(97-digit number)
10153656604534958577…64272679908107315201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.030 Γ— 10⁹⁢(97-digit number)
20307313209069917154…28545359816214630401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.061 Γ— 10⁹⁢(97-digit number)
40614626418139834308…57090719632429260801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.122 Γ— 10⁹⁢(97-digit number)
81229252836279668617…14181439264858521601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.624 Γ— 10⁹⁷(98-digit number)
16245850567255933723…28362878529717043201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.249 Γ— 10⁹⁷(98-digit number)
32491701134511867446…56725757059434086401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.498 Γ— 10⁹⁷(98-digit number)
64983402269023734893…13451514118868172801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.299 Γ— 10⁹⁸(99-digit number)
12996680453804746978…26903028237736345601
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 2646158

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 e866403ad4490c613ffda743691437c2540dcf692c3d6a7cd439567d36366ee9

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 #2,646,158 on Chainz β†—
Circulating Supply:57,936,568 XPMΒ·at block #6,836,537 Β· updates every 60s
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