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Home/Chain Registry/Block #2,756,095

Block #2,756,095

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/19/2018, 2:49:14 PM Β· Difficulty 11.6622 Β· 4,080,976 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f10120197f69b63d4c3dc95d23025a8d43bccf52bac7545957bc3b2820f7cf14
View on Chainz β†—

Difficulty

11.662186

Transactions

1

Size

200 B

Version

2

Bits

0ba98509

Nonce

778,123,223

Timestamp

7/19/2018, 2:49:14 PM

Confirmations

4,080,976

Merkle Root

2c4075bc2de1439afee8159d8420f163e2bd254db9a1dd06bf6c2889c2aecedc
Transactions (1)
Coinbase2c4075bc2de143…6c2889c2aecedc
1 in β†’ 1 out7.3400 XPM110 B
AdcfTq2R…79DiZGCW
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.

1.311 Γ— 10⁹⁡(96-digit number)
13112698135549422647…10303813567179826560
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
1.311 Γ— 10⁹⁡(96-digit number)
13112698135549422647…10303813567179826561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.622 Γ— 10⁹⁡(96-digit number)
26225396271098845294…20607627134359653121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.245 Γ— 10⁹⁡(96-digit number)
52450792542197690588…41215254268719306241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.049 Γ— 10⁹⁢(97-digit number)
10490158508439538117…82430508537438612481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.098 Γ— 10⁹⁢(97-digit number)
20980317016879076235…64861017074877224961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.196 Γ— 10⁹⁢(97-digit number)
41960634033758152470…29722034149754449921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.392 Γ— 10⁹⁢(97-digit number)
83921268067516304940…59444068299508899841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.678 Γ— 10⁹⁷(98-digit number)
16784253613503260988…18888136599017799681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.356 Γ— 10⁹⁷(98-digit number)
33568507227006521976…37776273198035599361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.713 Γ— 10⁹⁷(98-digit number)
67137014454013043952…75552546396071198721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.342 Γ— 10⁹⁸(99-digit number)
13427402890802608790…51105092792142397441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
2.685 Γ— 10⁹⁸(99-digit number)
26854805781605217581…02210185584284794881
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 2756095

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 f10120197f69b63d4c3dc95d23025a8d43bccf52bac7545957bc3b2820f7cf14

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 #2,756,095 on Chainz β†—
Circulating Supply:57,940,873 XPMΒ·at block #6,837,070 Β· updates every 60s
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