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Home/Chain Registry/Block #2,635,592

Block #2,635,592

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 4/29/2018, 7:19:36 AM Β· Difficulty 11.3265 Β· 4,195,303 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
83e8359178946b4a02cfcb8f1e6f7039a297ed2d36c648f5293fc367a8b0365d
View on Chainz β†—

Difficulty

11.326465

Transactions

1

Size

200 B

Version

2

Bits

0b53932e

Nonce

592,139,214

Timestamp

4/29/2018, 7:19:36 AM

Confirmations

4,195,303

Merkle Root

8e043863d6fa5afb2a46832694fd7d1b6b2571ee3b65aca52d1b18c9c5d17fc0
Transactions (1)
Coinbase8e043863d6fa5a…1b18c9c5d17fc0
1 in β†’ 1 out7.7800 XPM109 B
AaRnVAso…67JzRa5m
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.

3.440 Γ— 10⁹⁢(97-digit number)
34405237587047865019…47283075398149283840
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
3.440 Γ— 10⁹⁢(97-digit number)
34405237587047865019…47283075398149283839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.881 Γ— 10⁹⁢(97-digit number)
68810475174095730039…94566150796298567679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.376 Γ— 10⁹⁷(98-digit number)
13762095034819146007…89132301592597135359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.752 Γ— 10⁹⁷(98-digit number)
27524190069638292015…78264603185194270719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.504 Γ— 10⁹⁷(98-digit number)
55048380139276584031…56529206370388541439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.100 Γ— 10⁹⁸(99-digit number)
11009676027855316806…13058412740777082879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.201 Γ— 10⁹⁸(99-digit number)
22019352055710633612…26116825481554165759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.403 Γ— 10⁹⁸(99-digit number)
44038704111421267225…52233650963108331519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.807 Γ— 10⁹⁸(99-digit number)
88077408222842534450…04467301926216663039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.761 Γ— 10⁹⁹(100-digit number)
17615481644568506890…08934603852433326079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.523 Γ— 10⁹⁹(100-digit number)
35230963289137013780…17869207704866652159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
7.046 Γ— 10⁹⁹(100-digit number)
70461926578274027560…35738415409733304319
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2635592

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 83e8359178946b4a02cfcb8f1e6f7039a297ed2d36c648f5293fc367a8b0365d

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 #2,635,592 on Chainz β†—
Circulating Supply:57,891,287 XPMΒ·at block #6,830,894 Β· updates every 60s
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