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Home/Chain Registry/Block #2,653,092

Block #2,653,092

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/8/2018, 2:55:35 AM Β· Difficulty 11.7408 Β· 4,189,409 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2ae5e7ae3533f0e17bd33ebc439586a36ccc958b6b28046b979a76829bd6109b
View on Chainz β†—

Difficulty

11.740806

Transactions

2

Size

721 B

Version

2

Bits

0bbda578

Nonce

1,457,589,286

Timestamp

5/8/2018, 2:55:35 AM

Confirmations

4,189,409

Merkle Root

79df153799d5c5344b1bbda0e88f3a9c1c7db8928ecdba25bc121287c5f517ea
Transactions (2)
Coinbase0ae31911da9b31…3a4c83c2007033
1 in β†’ 1 out7.2500 XPM110 B
AHT6FGpC…4VgwJe71
b10e22b962eea2…c5c68ee3ee213e
3 in β†’ 2 out890.2437 XPM521 B
AU7xkW52…RMPvkSaUAQvCF7bF…FVvquQYi
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.

1.426 Γ— 10⁹⁡(96-digit number)
14266272687639205266…10656262254039600000
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
1.426 Γ— 10⁹⁡(96-digit number)
14266272687639205266…10656262254039600001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.853 Γ— 10⁹⁡(96-digit number)
28532545375278410532…21312524508079200001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.706 Γ— 10⁹⁡(96-digit number)
57065090750556821064…42625049016158400001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.141 Γ— 10⁹⁢(97-digit number)
11413018150111364212…85250098032316800001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.282 Γ— 10⁹⁢(97-digit number)
22826036300222728425…70500196064633600001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.565 Γ— 10⁹⁢(97-digit number)
45652072600445456851…41000392129267200001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.130 Γ— 10⁹⁢(97-digit number)
91304145200890913702…82000784258534400001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.826 Γ— 10⁹⁷(98-digit number)
18260829040178182740…64001568517068800001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.652 Γ— 10⁹⁷(98-digit number)
36521658080356365481…28003137034137600001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.304 Γ— 10⁹⁷(98-digit number)
73043316160712730962…56006274068275200001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.460 Γ— 10⁹⁸(99-digit number)
14608663232142546192…12012548136550400001
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 2653092

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 2ae5e7ae3533f0e17bd33ebc439586a36ccc958b6b28046b979a76829bd6109b

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 #2,653,092 on Chainz β†—
Circulating Supply:57,984,428 XPMΒ·at block #6,842,500 Β· updates every 60s
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