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Home/Chain Registry/Block #3,082,668

Block #3,082,668

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/7/2019, 3:49:51 PM Β· Difficulty 11.0229 Β· 3,760,436 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6b3c9e3a7fa29c848b88b3bdbec2530551c9fbb7c37f3d651fadb96db32f72c4
View on Chainz β†—

Difficulty

11.022874

Transactions

2

Size

1.14 KB

Version

2

Bits

0b05db0d

Nonce

189,208,159

Timestamp

3/7/2019, 3:49:51 PM

Confirmations

3,760,436

Merkle Root

86044749afe0e47c71d05845731346c194764450df3427932b0d9b3f21ba43e2
Transactions (2)
Coinbase0d73bdde730daa…0b70384c0d6008
1 in β†’ 1 out8.2400 XPM110 B
AbXwmGxD…4XXYP765
7baa9b9dd8c0db…a03f54d02edb3b
6 in β†’ 2 out861.6593 XPM968 B
AZQgL5kt…6NE43uZsAHFoXgQR…CmZ2JE4L
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.

2.213 Γ— 10⁹⁡(96-digit number)
22137016399575280885…18822326317678274400
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
2.213 Γ— 10⁹⁡(96-digit number)
22137016399575280885…18822326317678274399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.427 Γ— 10⁹⁡(96-digit number)
44274032799150561770…37644652635356548799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.854 Γ— 10⁹⁡(96-digit number)
88548065598301123540…75289305270713097599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.770 Γ— 10⁹⁢(97-digit number)
17709613119660224708…50578610541426195199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.541 Γ— 10⁹⁢(97-digit number)
35419226239320449416…01157221082852390399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.083 Γ— 10⁹⁢(97-digit number)
70838452478640898832…02314442165704780799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.416 Γ— 10⁹⁷(98-digit number)
14167690495728179766…04628884331409561599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.833 Γ— 10⁹⁷(98-digit number)
28335380991456359533…09257768662819123199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.667 Γ— 10⁹⁷(98-digit number)
56670761982912719066…18515537325638246399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.133 Γ— 10⁹⁸(99-digit number)
11334152396582543813…37031074651276492799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.266 Γ— 10⁹⁸(99-digit number)
22668304793165087626…74062149302552985599
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 3082668

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 6b3c9e3a7fa29c848b88b3bdbec2530551c9fbb7c37f3d651fadb96db32f72c4

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 #3,082,668 on Chainz β†—
Circulating Supply:57,989,196 XPMΒ·at block #6,843,103 Β· updates every 60s
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