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Home/Chain Registry/Block #2,726,194

Block #2,726,194

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 6/29/2018, 5:09:00 AM Β· Difficulty 11.6242 Β· 4,107,684 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
57305955ebd5e0201bda6643ab3a665227ecb19906d8ac676fc50488bfe88327
View on Chainz β†—

Difficulty

11.624232

Transactions

2

Size

7.33 KB

Version

2

Bits

0b9fcdb2

Nonce

156,794,135

Timestamp

6/29/2018, 5:09:00 AM

Confirmations

4,107,684

Merkle Root

47208f6f79f4f4a7b02b14a284d8ba37c72c05791c0dd413e45b27cd9b9b7de7
Transactions (2)
Coinbaseeae112c15b6816…4b4fc74cb9beee
1 in β†’ 1 out7.4700 XPM110 B
AKydWsxQ…mUHfH9ck
66c6ca77a63610…82fd8216e2fcae
49 in β†’ 2 out501.5534 XPM7.13 KB
AJcDB81D…ZX2on3CsAY6F4jD7…6NR2C2Mg
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.

1.161 Γ— 10⁹⁴(95-digit number)
11619974934106358736…17156686482338365440
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
1.161 Γ— 10⁹⁴(95-digit number)
11619974934106358736…17156686482338365439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.323 Γ— 10⁹⁴(95-digit number)
23239949868212717472…34313372964676730879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.647 Γ— 10⁹⁴(95-digit number)
46479899736425434945…68626745929353461759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.295 Γ— 10⁹⁴(95-digit number)
92959799472850869891…37253491858706923519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.859 Γ— 10⁹⁡(96-digit number)
18591959894570173978…74506983717413847039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.718 Γ— 10⁹⁡(96-digit number)
37183919789140347956…49013967434827694079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.436 Γ— 10⁹⁡(96-digit number)
74367839578280695913…98027934869655388159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.487 Γ— 10⁹⁢(97-digit number)
14873567915656139182…96055869739310776319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.974 Γ— 10⁹⁢(97-digit number)
29747135831312278365…92111739478621552639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.949 Γ— 10⁹⁢(97-digit number)
59494271662624556730…84223478957243105279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.189 Γ— 10⁹⁷(98-digit number)
11898854332524911346…68446957914486210559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
2.379 Γ— 10⁹⁷(98-digit number)
23797708665049822692…36893915828972421119
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 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
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 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 2726194

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 57305955ebd5e0201bda6643ab3a665227ecb19906d8ac676fc50488bfe88327

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 #2,726,194 on Chainz β†—
Circulating Supply:57,915,257 XPMΒ·at block #6,833,877 Β· updates every 60s
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