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Home/Chain Registry/Block #3,506,348

Block #3,506,348

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/9/2020, 6:22:55 AM Β· Difficulty 10.9305 Β· 3,320,467 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3211f49607429ca4918b397fa6cb51a24a3d2710874d0023b7bbefd13493ff11
View on Chainz β†—

Difficulty

10.930502

Transactions

1

Size

200 B

Version

2

Bits

0aee3564

Nonce

200,387,670

Timestamp

1/9/2020, 6:22:55 AM

Confirmations

3,320,467

Merkle Root

b82404722dd21d15e1f57aa5c970e49d779f6d883250bc48bf64a13894ed34ec
Transactions (1)
Coinbaseb82404722dd21d…64a13894ed34ec
1 in β†’ 1 out8.3600 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.

1.102 Γ— 10⁹⁴(95-digit number)
11025057091584424988…03215911573188782720
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
1.102 Γ— 10⁹⁴(95-digit number)
11025057091584424988…03215911573188782721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.205 Γ— 10⁹⁴(95-digit number)
22050114183168849976…06431823146377565441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.410 Γ— 10⁹⁴(95-digit number)
44100228366337699953…12863646292755130881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.820 Γ— 10⁹⁴(95-digit number)
88200456732675399906…25727292585510261761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.764 Γ— 10⁹⁡(96-digit number)
17640091346535079981…51454585171020523521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.528 Γ— 10⁹⁡(96-digit number)
35280182693070159962…02909170342041047041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.056 Γ— 10⁹⁡(96-digit number)
70560365386140319925…05818340684082094081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.411 Γ— 10⁹⁢(97-digit number)
14112073077228063985…11636681368164188161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.822 Γ— 10⁹⁢(97-digit number)
28224146154456127970…23273362736328376321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.644 Γ— 10⁹⁢(97-digit number)
56448292308912255940…46546725472656752641
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 3506348

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 3211f49607429ca4918b397fa6cb51a24a3d2710874d0023b7bbefd13493ff11

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 #3,506,348 on Chainz β†—
Circulating Supply:57,858,683 XPMΒ·at block #6,826,814 Β· updates every 60s
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