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Block #1,378,523

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/21/2015, 10:30:18 AM Β· Difficulty 10.8102 Β· 5,447,919 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0dbd654dca6acbb50418cdd308ea8c90814582e4241cd63ca2e43aa7a5902f52
View on Chainz β†—

Difficulty

10.810242

Transactions

1

Size

200 B

Version

2

Bits

0acf6c05

Nonce

1,292,941,040

Timestamp

12/21/2015, 10:30:18 AM

Confirmations

5,447,919

Merkle Root

86f19f92714893da95fc7c91f6f9422cc52b45317f1009aec48abe9c8eb6dc40
Transactions (1)
Coinbase86f19f92714893…8abe9c8eb6dc40
1 in β†’ 1 out8.5400 XPM110 B
AQ8PfZwS…G5mfgu8V
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.

7.905 Γ— 10⁹⁡(96-digit number)
79054411787637096277…98772481871241966400
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
7.905 Γ— 10⁹⁡(96-digit number)
79054411787637096277…98772481871241966401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.581 Γ— 10⁹⁢(97-digit number)
15810882357527419255…97544963742483932801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.162 Γ— 10⁹⁢(97-digit number)
31621764715054838511…95089927484967865601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.324 Γ— 10⁹⁢(97-digit number)
63243529430109677022…90179854969935731201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.264 Γ— 10⁹⁷(98-digit number)
12648705886021935404…80359709939871462401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.529 Γ— 10⁹⁷(98-digit number)
25297411772043870808…60719419879742924801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.059 Γ— 10⁹⁷(98-digit number)
50594823544087741617…21438839759485849601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.011 Γ— 10⁹⁸(99-digit number)
10118964708817548323…42877679518971699201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.023 Γ— 10⁹⁸(99-digit number)
20237929417635096647…85755359037943398401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.047 Γ— 10⁹⁸(99-digit number)
40475858835270193294…71510718075886796801
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1378523

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 0dbd654dca6acbb50418cdd308ea8c90814582e4241cd63ca2e43aa7a5902f52

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 #1,378,523 on Chainz β†—
Circulating Supply:57,855,673 XPMΒ·at block #6,826,441 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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