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Home/Chain Registry/Block #2,819,103

Block #2,819,103

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/31/2018, 11:07:07 PM Β· Difficulty 11.7013 Β· 4,020,529 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ef2ecb78fb2e6034b44e3dc4ef81954b7b5acbce2bca3650a3a36f45821b9d5d
View on Chainz β†—

Difficulty

11.701290

Transactions

1

Size

201 B

Version

2

Bits

0bb387c1

Nonce

26,912,027

Timestamp

8/31/2018, 11:07:07 PM

Confirmations

4,020,529

Merkle Root

24e4591d8ebbb53e618935e4f8f7a3dad8533ed0e15ba62b124ed4a087a0cd48
Transactions (1)
Coinbase24e4591d8ebbb5…4ed4a087a0cd48
1 in β†’ 1 out7.2900 XPM110 B
AZtxQr2F…7grUWrUz
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.

1.563 Γ— 10⁹⁢(97-digit number)
15634213655585293860…13321947440939888640
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
1.563 Γ— 10⁹⁢(97-digit number)
15634213655585293860…13321947440939888641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.126 Γ— 10⁹⁢(97-digit number)
31268427311170587721…26643894881879777281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.253 Γ— 10⁹⁢(97-digit number)
62536854622341175442…53287789763759554561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.250 Γ— 10⁹⁷(98-digit number)
12507370924468235088…06575579527519109121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.501 Γ— 10⁹⁷(98-digit number)
25014741848936470176…13151159055038218241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.002 Γ— 10⁹⁷(98-digit number)
50029483697872940353…26302318110076436481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.000 Γ— 10⁹⁸(99-digit number)
10005896739574588070…52604636220152872961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.001 Γ— 10⁹⁸(99-digit number)
20011793479149176141…05209272440305745921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.002 Γ— 10⁹⁸(99-digit number)
40023586958298352283…10418544880611491841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.004 Γ— 10⁹⁸(99-digit number)
80047173916596704566…20837089761222983681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.600 Γ— 10⁹⁹(100-digit number)
16009434783319340913…41674179522445967361
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 2819103

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 ef2ecb78fb2e6034b44e3dc4ef81954b7b5acbce2bca3650a3a36f45821b9d5d

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 #2,819,103 on Chainz β†—
Circulating Supply:57,961,349 XPMΒ·at block #6,839,631 Β· updates every 60s
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