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Home/Chain Registry/Block #3,655,205

Block #3,655,205

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/23/2020, 10:29:13 AM Β· Difficulty 10.8902 Β· 3,186,994 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6a7517b05fad25e290a7a0c5fd780ca774f6872a298cd79e94263d1784ea786a
View on Chainz β†—

Difficulty

10.890174

Transactions

1

Size

201 B

Version

2

Bits

0ae3e279

Nonce

201,912,622

Timestamp

4/23/2020, 10:29:13 AM

Confirmations

3,186,994

Merkle Root

60d7becfad80cca2f5f0d83b5d1b05faa25ce40183e6508d2939c838d51c64ab
Transactions (1)
Coinbase60d7becfad80cc…39c838d51c64ab
1 in β†’ 1 out8.4200 XPM110 B
AbQi6wWz…Vjdi6XdX
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.

4.529 Γ— 10⁹⁷(98-digit number)
45296489184472472919…76099040408415027200
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
4.529 Γ— 10⁹⁷(98-digit number)
45296489184472472919…76099040408415027201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.059 Γ— 10⁹⁷(98-digit number)
90592978368944945839…52198080816830054401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.811 Γ— 10⁹⁸(99-digit number)
18118595673788989167…04396161633660108801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.623 Γ— 10⁹⁸(99-digit number)
36237191347577978335…08792323267320217601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.247 Γ— 10⁹⁸(99-digit number)
72474382695155956671…17584646534640435201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.449 Γ— 10⁹⁹(100-digit number)
14494876539031191334…35169293069280870401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.898 Γ— 10⁹⁹(100-digit number)
28989753078062382668…70338586138561740801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.797 Γ— 10⁹⁹(100-digit number)
57979506156124765337…40677172277123481601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.159 Γ— 10¹⁰⁰(101-digit number)
11595901231224953067…81354344554246963201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.319 Γ— 10¹⁰⁰(101-digit number)
23191802462449906134…62708689108493926401
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 3655205

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 6a7517b05fad25e290a7a0c5fd780ca774f6872a298cd79e94263d1784ea786a

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 #3,655,205 on Chainz β†—
Circulating Supply:57,981,986 XPMΒ·at block #6,842,198 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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