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Home/Chain Registry/Block #3,225,397

Block #3,225,397

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/14/2019, 8:40:23 PM Β· Difficulty 11.0069 Β· 3,611,357 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4d21fc83e18d26ece075235848b7cf759d2d3450e6303e706a67525afb0768a5
View on Chainz β†—

Difficulty

11.006940

Transactions

2

Size

1.43 KB

Version

2

Bits

0b01c6d2

Nonce

2,121,263,044

Timestamp

6/14/2019, 8:40:23 PM

Confirmations

3,611,357

Merkle Root

3d48649209a8ae995dabeddecd354514c497b5131c812bc5b1173558cd489085
Transactions (2)
Coinbasecb4ef956a99965…561ce9cac7e18e
1 in β†’ 1 out8.2600 XPM110 B
ARbm48qR…9xQc8DBX
1381c2f05427d6…5ed3ee8ef96d4d
8 in β†’ 2 out14.4371 XPM1.23 KB
AYKZRBfK…Qi1vAB2MAdByuHzS…duR62m5o
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.

5.691 Γ— 10⁹⁢(97-digit number)
56917158967472139944…97055009981894144000
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
5.691 Γ— 10⁹⁢(97-digit number)
56917158967472139944…97055009981894143999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.138 Γ— 10⁹⁷(98-digit number)
11383431793494427988…94110019963788287999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.276 Γ— 10⁹⁷(98-digit number)
22766863586988855977…88220039927576575999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.553 Γ— 10⁹⁷(98-digit number)
45533727173977711955…76440079855153151999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.106 Γ— 10⁹⁷(98-digit number)
91067454347955423910…52880159710306303999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.821 Γ— 10⁹⁸(99-digit number)
18213490869591084782…05760319420612607999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.642 Γ— 10⁹⁸(99-digit number)
36426981739182169564…11520638841225215999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.285 Γ— 10⁹⁸(99-digit number)
72853963478364339128…23041277682450431999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.457 Γ— 10⁹⁹(100-digit number)
14570792695672867825…46082555364900863999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.914 Γ— 10⁹⁹(100-digit number)
29141585391345735651…92165110729801727999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.828 Γ— 10⁹⁹(100-digit number)
58283170782691471302…84330221459603455999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 3225397

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 4d21fc83e18d26ece075235848b7cf759d2d3450e6303e706a67525afb0768a5

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 #3,225,397 on Chainz β†—
Circulating Supply:57,938,318 XPMΒ·at block #6,836,753 Β· updates every 60s
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