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Home/Chain Registry/Block #2,655,578

Block #2,655,578

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/10/2018, 7:28:31 AM Β· Difficulty 11.7043 Β· 4,178,257 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cbd83130d633b55cb8af375b5cc657638747e534be606a8791253d85301a0a0c
View on Chainz β†—

Difficulty

11.704303

Transactions

2

Size

724 B

Version

2

Bits

0bb44d2d

Nonce

934,880,805

Timestamp

5/10/2018, 7:28:31 AM

Confirmations

4,178,257

Merkle Root

22594081df62e00ca0b9c7f4445dc4e7a558397c889ab1f8cdcf4b2705887efd
Transactions (2)
Coinbasee8011273745d35…ea81a029ff10cd
1 in β†’ 1 out7.3000 XPM110 B
Aahp1nAg…aF5FGzXE
3b18b483947ed3…c1ae510e06d36b
3 in β†’ 2 out294.4263 XPM524 B
AaoVyS59…FvfsDsDvAcZWxwzp…MURizaF7
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.

8.141 Γ— 10⁹⁴(95-digit number)
81411577011091618639…73157281581559168640
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
8.141 Γ— 10⁹⁴(95-digit number)
81411577011091618639…73157281581559168639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.628 Γ— 10⁹⁡(96-digit number)
16282315402218323727…46314563163118337279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.256 Γ— 10⁹⁡(96-digit number)
32564630804436647455…92629126326236674559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.512 Γ— 10⁹⁡(96-digit number)
65129261608873294911…85258252652473349119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.302 Γ— 10⁹⁢(97-digit number)
13025852321774658982…70516505304946698239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.605 Γ— 10⁹⁢(97-digit number)
26051704643549317964…41033010609893396479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.210 Γ— 10⁹⁢(97-digit number)
52103409287098635929…82066021219786792959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.042 Γ— 10⁹⁷(98-digit number)
10420681857419727185…64132042439573585919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.084 Γ— 10⁹⁷(98-digit number)
20841363714839454371…28264084879147171839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.168 Γ— 10⁹⁷(98-digit number)
41682727429678908743…56528169758294343679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.336 Γ— 10⁹⁷(98-digit number)
83365454859357817486…13056339516588687359
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 2655578

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 cbd83130d633b55cb8af375b5cc657638747e534be606a8791253d85301a0a0c

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 #2,655,578 on Chainz β†—
Circulating Supply:57,914,908 XPMΒ·at block #6,833,834 Β· updates every 60s
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