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Block #2,658,245

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/12/2018, 4:50:55 PM Β· Difficulty 11.6552 Β· 4,187,136 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c55de768f9f46382850960cba000aee892d0626e980cfeefcb2235275d87ca2e
View on Chainz β†—

Difficulty

11.655215

Transactions

1

Size

200 B

Version

2

Bits

0ba7bc2e

Nonce

262,358,926

Timestamp

5/12/2018, 4:50:55 PM

Confirmations

4,187,136

Merkle Root

02be30d3a4d9c5ef2d9da151927e609ba693bafe517b2bee10d586cf88cd9f34
Transactions (1)
Coinbase02be30d3a4d9c5…d586cf88cd9f34
1 in β†’ 1 out7.3500 XPM110 B
Adqah8zh…1WwoHJ9t
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.

8.860 Γ— 10⁹⁴(95-digit number)
88607721472920005602…97150633743358127120
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
8.860 Γ— 10⁹⁴(95-digit number)
88607721472920005602…97150633743358127119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.772 Γ— 10⁹⁡(96-digit number)
17721544294584001120…94301267486716254239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.544 Γ— 10⁹⁡(96-digit number)
35443088589168002240…88602534973432508479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.088 Γ— 10⁹⁡(96-digit number)
70886177178336004481…77205069946865016959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.417 Γ— 10⁹⁢(97-digit number)
14177235435667200896…54410139893730033919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.835 Γ— 10⁹⁢(97-digit number)
28354470871334401792…08820279787460067839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.670 Γ— 10⁹⁢(97-digit number)
56708941742668803585…17640559574920135679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.134 Γ— 10⁹⁷(98-digit number)
11341788348533760717…35281119149840271359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.268 Γ— 10⁹⁷(98-digit number)
22683576697067521434…70562238299680542719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.536 Γ— 10⁹⁷(98-digit number)
45367153394135042868…41124476599361085439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.073 Γ— 10⁹⁷(98-digit number)
90734306788270085736…82248953198722170879
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 2658245

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 c55de768f9f46382850960cba000aee892d0626e980cfeefcb2235275d87ca2e

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 #2,658,245 on Chainz β†—
Circulating Supply:58,007,493 XPMΒ·at block #6,845,380 Β· updates every 60s
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