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Block #3,085,462

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/9/2019, 1:42:34 PM Β· Difficulty 11.0309 Β· 3,754,885 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b68e0cf9584e726ac394ea2afdc271cfc502e82319cbd4e58196043db3fe789c
View on Chainz β†—

Difficulty

11.030873

Transactions

1

Size

200 B

Version

2

Bits

0b07e750

Nonce

172,470,880

Timestamp

3/9/2019, 1:42:34 PM

Confirmations

3,754,885

Merkle Root

2d53e62b894a9da2932871a544e406a8b080c0385bfb3ee8c557ded901dd2d52
Transactions (1)
Coinbase2d53e62b894a9d…57ded901dd2d52
1 in β†’ 1 out8.2100 XPM109 B
AUMQRepm…tAfKmdW1
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.

4.231 Γ— 10⁹⁢(97-digit number)
42310838484100624856…87256553964370440320
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
4.231 Γ— 10⁹⁢(97-digit number)
42310838484100624856…87256553964370440319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.462 Γ— 10⁹⁢(97-digit number)
84621676968201249712…74513107928740880639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.692 Γ— 10⁹⁷(98-digit number)
16924335393640249942…49026215857481761279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.384 Γ— 10⁹⁷(98-digit number)
33848670787280499884…98052431714963522559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.769 Γ— 10⁹⁷(98-digit number)
67697341574560999769…96104863429927045119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.353 Γ— 10⁹⁸(99-digit number)
13539468314912199953…92209726859854090239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.707 Γ— 10⁹⁸(99-digit number)
27078936629824399907…84419453719708180479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.415 Γ— 10⁹⁸(99-digit number)
54157873259648799815…68838907439416360959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.083 Γ— 10⁹⁹(100-digit number)
10831574651929759963…37677814878832721919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.166 Γ— 10⁹⁹(100-digit number)
21663149303859519926…75355629757665443839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.332 Γ— 10⁹⁹(100-digit number)
43326298607719039852…50711259515330887679
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 3085462

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 b68e0cf9584e726ac394ea2afdc271cfc502e82319cbd4e58196043db3fe789c

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 #3,085,462 on Chainz β†—
Circulating Supply:57,967,098 XPMΒ·at block #6,840,346 Β· updates every 60s
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