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Home/Chain Registry/Block #3,518,598

Block #3,518,598

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/17/2020, 1:34:41 PM Β· Difficulty 10.9348 Β· 3,306,289 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1bd10626ffa7e4806014e08ad65a396742b36837d849149a71ae376fc12a5bd8
View on Chainz β†—

Difficulty

10.934843

Transactions

1

Size

200 B

Version

2

Bits

0aef51dd

Nonce

156,162,545

Timestamp

1/17/2020, 1:34:41 PM

Confirmations

3,306,289

Merkle Root

b9e93fb79785e23c9cd0568da0613dac6acce9917b4487575ba1abeca29db3a4
Transactions (1)
Coinbaseb9e93fb79785e2…a1abeca29db3a4
1 in β†’ 1 out8.3500 XPM110 B
ASiq2qtK…VMhmk7yL
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.

5.571 Γ— 10⁹⁴(95-digit number)
55714675118996554435…16338312000678176000
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
5.571 Γ— 10⁹⁴(95-digit number)
55714675118996554435…16338312000678175999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.114 Γ— 10⁹⁡(96-digit number)
11142935023799310887…32676624001356351999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.228 Γ— 10⁹⁡(96-digit number)
22285870047598621774…65353248002712703999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.457 Γ— 10⁹⁡(96-digit number)
44571740095197243548…30706496005425407999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.914 Γ— 10⁹⁡(96-digit number)
89143480190394487096…61412992010850815999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.782 Γ— 10⁹⁢(97-digit number)
17828696038078897419…22825984021701631999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.565 Γ— 10⁹⁢(97-digit number)
35657392076157794838…45651968043403263999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.131 Γ— 10⁹⁢(97-digit number)
71314784152315589676…91303936086806527999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.426 Γ— 10⁹⁷(98-digit number)
14262956830463117935…82607872173613055999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.852 Γ— 10⁹⁷(98-digit number)
28525913660926235870…65215744347226111999
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 3518598

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 1bd10626ffa7e4806014e08ad65a396742b36837d849149a71ae376fc12a5bd8

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 #3,518,598 on Chainz β†—
Circulating Supply:57,843,177 XPMΒ·at block #6,824,886 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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