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Home/Chain Registry/Block #3,506,065

Block #3,506,065

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/9/2020, 1:50:55 AM Β· Difficulty 10.9303 Β· 3,337,660 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2ea85bc7b73b0937caae694cf9b9b8be808972312971b940e79d41708277de4b
View on Chainz β†—

Difficulty

10.930324

Transactions

1

Size

199 B

Version

2

Bits

0aee29bb

Nonce

1,953,460,769

Timestamp

1/9/2020, 1:50:55 AM

Confirmations

3,337,660

Merkle Root

f54940dc59a79e725bf4eeaf68f13e6f179b2d8dde16025582828ee9f19baee7
Transactions (1)
Coinbasef54940dc59a79e…828ee9f19baee7
1 in β†’ 1 out8.3600 XPM109 B
AXfJqzUb…HXeXmjMz
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.

2.142 Γ— 10⁹⁡(96-digit number)
21421231364592879370…25551373301330007040
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
2.142 Γ— 10⁹⁡(96-digit number)
21421231364592879370…25551373301330007039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.284 Γ— 10⁹⁡(96-digit number)
42842462729185758740…51102746602660014079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.568 Γ— 10⁹⁡(96-digit number)
85684925458371517480…02205493205320028159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.713 Γ— 10⁹⁢(97-digit number)
17136985091674303496…04410986410640056319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.427 Γ— 10⁹⁢(97-digit number)
34273970183348606992…08821972821280112639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.854 Γ— 10⁹⁢(97-digit number)
68547940366697213984…17643945642560225279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.370 Γ— 10⁹⁷(98-digit number)
13709588073339442796…35287891285120450559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.741 Γ— 10⁹⁷(98-digit number)
27419176146678885593…70575782570240901119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.483 Γ— 10⁹⁷(98-digit number)
54838352293357771187…41151565140481802239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.096 Γ— 10⁹⁸(99-digit number)
10967670458671554237…82303130280963604479
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 3506065

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 2ea85bc7b73b0937caae694cf9b9b8be808972312971b940e79d41708277de4b

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 #3,506,065 on Chainz β†—
Circulating Supply:57,994,171 XPMΒ·at block #6,843,724 Β· updates every 60s
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