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Home/Chain Registry/Block #3,085,412

Block #3,085,412

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/9/2019, 12:45:46 PM Β· Difficulty 11.0321 Β· 3,756,704 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7704b9cab18a07d92a691a225ffe47c2ba81a3d5d444ba132ea45b287b0b45d4
View on Chainz β†—

Difficulty

11.032097

Transactions

1

Size

201 B

Version

2

Bits

0b083787

Nonce

724,035,923

Timestamp

3/9/2019, 12:45:46 PM

Confirmations

3,756,704

Merkle Root

16eb7cdb9e54b85e4a09e1c4af741a92b21076045ca1e2db215d5c611b57b991
Transactions (1)
Coinbase16eb7cdb9e54b8…5d5c611b57b991
1 in β†’ 1 out8.2000 XPM110 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.

6.530 Γ— 10⁹⁢(97-digit number)
65307191434695845806…65673546723611381760
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
6.530 Γ— 10⁹⁢(97-digit number)
65307191434695845806…65673546723611381759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.306 Γ— 10⁹⁷(98-digit number)
13061438286939169161…31347093447222763519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.612 Γ— 10⁹⁷(98-digit number)
26122876573878338322…62694186894445527039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.224 Γ— 10⁹⁷(98-digit number)
52245753147756676645…25388373788891054079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.044 Γ— 10⁹⁸(99-digit number)
10449150629551335329…50776747577782108159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.089 Γ— 10⁹⁸(99-digit number)
20898301259102670658…01553495155564216319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.179 Γ— 10⁹⁸(99-digit number)
41796602518205341316…03106990311128432639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.359 Γ— 10⁹⁸(99-digit number)
83593205036410682632…06213980622256865279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.671 Γ— 10⁹⁹(100-digit number)
16718641007282136526…12427961244513730559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.343 Γ— 10⁹⁹(100-digit number)
33437282014564273052…24855922489027461119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.687 Γ— 10⁹⁹(100-digit number)
66874564029128546105…49711844978054922239
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 3085412

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 7704b9cab18a07d92a691a225ffe47c2ba81a3d5d444ba132ea45b287b0b45d4

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 #3,085,412 on Chainz β†—
Circulating Supply:57,981,314 XPMΒ·at block #6,842,115 Β· updates every 60s
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