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Home/Chain Registry/Block #2,043,422

Block #2,043,422

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/29/2017, 9:26:53 AM Β· Difficulty 10.6750 Β· 4,799,949 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6fa21a3939c75de02ffe49a0ea31327fc2e73baa77a1a0da0486a4676a2c0571
View on Chainz β†—

Difficulty

10.675026

Transactions

1

Size

201 B

Version

2

Bits

0aacce84

Nonce

2,091,437,457

Timestamp

3/29/2017, 9:26:53 AM

Confirmations

4,799,949

Merkle Root

37313084f05b01910c407efced0876efc8f5276ba959655023bd32294785844c
Transactions (1)
Coinbase37313084f05b01…bd32294785844c
1 in β†’ 1 out8.7600 XPM110 B
AJ8ALWXm…T4pAuJEa
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.

1.818 Γ— 10⁹⁢(97-digit number)
18181188717233358588…33087473891072296960
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
1.818 Γ— 10⁹⁢(97-digit number)
18181188717233358588…33087473891072296959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.636 Γ— 10⁹⁢(97-digit number)
36362377434466717176…66174947782144593919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.272 Γ— 10⁹⁢(97-digit number)
72724754868933434352…32349895564289187839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.454 Γ— 10⁹⁷(98-digit number)
14544950973786686870…64699791128578375679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.908 Γ— 10⁹⁷(98-digit number)
29089901947573373741…29399582257156751359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.817 Γ— 10⁹⁷(98-digit number)
58179803895146747482…58799164514313502719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.163 Γ— 10⁹⁸(99-digit number)
11635960779029349496…17598329028627005439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.327 Γ— 10⁹⁸(99-digit number)
23271921558058698992…35196658057254010879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.654 Γ— 10⁹⁸(99-digit number)
46543843116117397985…70393316114508021759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.308 Γ— 10⁹⁸(99-digit number)
93087686232234795971…40786632229016043519
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 2043422

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 6fa21a3939c75de02ffe49a0ea31327fc2e73baa77a1a0da0486a4676a2c0571

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 #2,043,422 on Chainz β†—
Circulating Supply:57,991,332 XPMΒ·at block #6,843,370 Β· updates every 60s
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