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Block #2,468,488

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/11/2018, 8:31:59 PM Β· Difficulty 10.9602 Β· 4,375,984 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7ce147677a2d81737b0dc94ff54f721d4e5fdcec617f943db68323da41f082ad
View on Chainz β†—

Difficulty

10.960178

Transactions

1

Size

198 B

Version

2

Bits

0af5ce3f

Nonce

1,927,559,890

Timestamp

1/11/2018, 8:31:59 PM

Confirmations

4,375,984

Merkle Root

980b4209a6643652170f6aacc1f10e96e2e0348603374121cce7a96808a3d573
Transactions (1)
Coinbase980b4209a66436…e7a96808a3d573
1 in β†’ 1 out8.3100 XPM109 B
AbDRRfoN…hZzk5tJw
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.

8.541 Γ— 10⁹¹(92-digit number)
85418482917395341645…01598732817540053120
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
8.541 Γ— 10⁹¹(92-digit number)
85418482917395341645…01598732817540053119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.708 Γ— 10⁹²(93-digit number)
17083696583479068329…03197465635080106239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.416 Γ— 10⁹²(93-digit number)
34167393166958136658…06394931270160212479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.833 Γ— 10⁹²(93-digit number)
68334786333916273316…12789862540320424959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.366 Γ— 10⁹³(94-digit number)
13666957266783254663…25579725080640849919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.733 Γ— 10⁹³(94-digit number)
27333914533566509326…51159450161281699839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.466 Γ— 10⁹³(94-digit number)
54667829067133018652…02318900322563399679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.093 Γ— 10⁹⁴(95-digit number)
10933565813426603730…04637800645126799359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.186 Γ— 10⁹⁴(95-digit number)
21867131626853207461…09275601290253598719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.373 Γ— 10⁹⁴(95-digit number)
43734263253706414922…18551202580507197439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.746 Γ— 10⁹⁴(95-digit number)
87468526507412829844…37102405161014394879
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 2468488

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 7ce147677a2d81737b0dc94ff54f721d4e5fdcec617f943db68323da41f082ad

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 #2,468,488 on Chainz β†—
Circulating Supply:58,000,171 XPMΒ·at block #6,844,471 Β· updates every 60s
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