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Home/Chain Registry/Block #2,094,789

Block #2,094,789

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2017, 8:39:27 PM Β· Difficulty 10.8720 Β· 4,742,008 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8ae7b29771af2919c71a61bc9d1a4a67ce4d295649ee9376e825ea1a864487b6
View on Chainz β†—

Difficulty

10.871992

Transactions

2

Size

1.68 KB

Version

2

Bits

0adf3ad8

Nonce

804,783,937

Timestamp

4/30/2017, 8:39:27 PM

Confirmations

4,742,008

Merkle Root

f9841b7c27299ad07e9a7fcaa855902ae7737c700ccd3589c50cce583cc11291
Transactions (2)
Coinbase52c6ef56386fa2…bcfcde4ca47c94
1 in β†’ 1 out8.4800 XPM110 B
AQx1qaUB…vGXZBpbj
979a86f4fba838…2d9065ecc7b324
10 in β†’ 1 out8408.4569 XPM1.49 KB
AHKEqLWG…Z6JsKv41
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.

6.168 Γ— 10⁹⁴(95-digit number)
61686275828089242109…44009572927488924160
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
6.168 Γ— 10⁹⁴(95-digit number)
61686275828089242109…44009572927488924159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.233 Γ— 10⁹⁡(96-digit number)
12337255165617848421…88019145854977848319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.467 Γ— 10⁹⁡(96-digit number)
24674510331235696843…76038291709955696639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.934 Γ— 10⁹⁡(96-digit number)
49349020662471393687…52076583419911393279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.869 Γ— 10⁹⁡(96-digit number)
98698041324942787375…04153166839822786559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.973 Γ— 10⁹⁢(97-digit number)
19739608264988557475…08306333679645573119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.947 Γ— 10⁹⁢(97-digit number)
39479216529977114950…16612667359291146239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.895 Γ— 10⁹⁢(97-digit number)
78958433059954229900…33225334718582292479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.579 Γ— 10⁹⁷(98-digit number)
15791686611990845980…66450669437164584959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.158 Γ— 10⁹⁷(98-digit number)
31583373223981691960…32901338874329169919
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2094789

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 8ae7b29771af2919c71a61bc9d1a4a67ce4d295649ee9376e825ea1a864487b6

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 #2,094,789 on Chainz β†—
Circulating Supply:57,938,657 XPMΒ·at block #6,836,796 Β· updates every 60s
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