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Home/Chain Registry/Block #1,832,462

Block #1,832,462

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/2/2016, 7:30:01 AM Β· Difficulty 10.7154 Β· 5,000,536 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1136318da4748d595e005a48b1f4570fd6cd5e74a1137f19d3aeb70a67a60efd
View on Chainz β†—

Difficulty

10.715416

Transactions

2

Size

1.28 KB

Version

2

Bits

0ab72586

Nonce

457,660,227

Timestamp

11/2/2016, 7:30:01 AM

Confirmations

5,000,536

Merkle Root

aa2f80b4a6d5863526b9bc54b87d64cf39cf622bcd7eb8779d76bd39f780f288
Transactions (2)
Coinbasece373ca26347c8…78be47d37957d5
1 in β†’ 1 out8.7200 XPM109 B
ASBK5Qc6…7GUFGskB
e4b32ba9013075…57e80cd46c2bd4
7 in β†’ 2 out986.2268 XPM1.09 KB
AQwVFAvD…AuC591U2AZ7xo3ni…aXTAFhZR
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.

3.465 Γ— 10⁹⁢(97-digit number)
34650417352846152020…38452991240158561280
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
3.465 Γ— 10⁹⁢(97-digit number)
34650417352846152020…38452991240158561279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.930 Γ— 10⁹⁢(97-digit number)
69300834705692304040…76905982480317122559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.386 Γ— 10⁹⁷(98-digit number)
13860166941138460808…53811964960634245119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.772 Γ— 10⁹⁷(98-digit number)
27720333882276921616…07623929921268490239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.544 Γ— 10⁹⁷(98-digit number)
55440667764553843232…15247859842536980479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.108 Γ— 10⁹⁸(99-digit number)
11088133552910768646…30495719685073960959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.217 Γ— 10⁹⁸(99-digit number)
22176267105821537292…60991439370147921919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.435 Γ— 10⁹⁸(99-digit number)
44352534211643074585…21982878740295843839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.870 Γ— 10⁹⁸(99-digit number)
88705068423286149171…43965757480591687679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.774 Γ— 10⁹⁹(100-digit number)
17741013684657229834…87931514961183375359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.548 Γ— 10⁹⁹(100-digit number)
35482027369314459668…75863029922366750719
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 1832462

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 1136318da4748d595e005a48b1f4570fd6cd5e74a1137f19d3aeb70a67a60efd

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 #1,832,462 on Chainz β†—
Circulating Supply:57,908,156 XPMΒ·at block #6,832,997 Β· updates every 60s
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