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Home/Chain Registry/Block #2,495,194

Block #2,495,194

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/29/2018, 1:30:33 AM Β· Difficulty 10.9735 Β· 4,344,233 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
919ddecaa4c2a031cd1f736d4045e7eb494a9e9bdaa474694ff815a39a5c60ad
View on Chainz β†—

Difficulty

10.973484

Transactions

1

Size

199 B

Version

2

Bits

0af93647

Nonce

884,062,032

Timestamp

1/29/2018, 1:30:33 AM

Confirmations

4,344,233

Merkle Root

bf583c5faf0fd96eb35006fa6f6ca01f05c09477f20982b3d56e839eeb0ee25e
Transactions (1)
Coinbasebf583c5faf0fd9…6e839eeb0ee25e
1 in β†’ 1 out8.2900 XPM109 B
AeSuMohB…9QFaQpzv
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.

4.024 Γ— 10⁹³(94-digit number)
40240823028211478439…13601644552970649600
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
4.024 Γ— 10⁹³(94-digit number)
40240823028211478439…13601644552970649599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.048 Γ— 10⁹³(94-digit number)
80481646056422956879…27203289105941299199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.609 Γ— 10⁹⁴(95-digit number)
16096329211284591375…54406578211882598399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.219 Γ— 10⁹⁴(95-digit number)
32192658422569182751…08813156423765196799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.438 Γ— 10⁹⁴(95-digit number)
64385316845138365503…17626312847530393599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.287 Γ— 10⁹⁡(96-digit number)
12877063369027673100…35252625695060787199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.575 Γ— 10⁹⁡(96-digit number)
25754126738055346201…70505251390121574399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.150 Γ— 10⁹⁡(96-digit number)
51508253476110692402…41010502780243148799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.030 Γ— 10⁹⁢(97-digit number)
10301650695222138480…82021005560486297599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.060 Γ— 10⁹⁢(97-digit number)
20603301390444276961…64042011120972595199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.120 Γ— 10⁹⁢(97-digit number)
41206602780888553922…28084022241945190399
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2495194

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 919ddecaa4c2a031cd1f736d4045e7eb494a9e9bdaa474694ff815a39a5c60ad

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 #2,495,194 on Chainz β†—
Circulating Supply:57,959,705 XPMΒ·at block #6,839,426 Β· updates every 60s
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