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Home/Chain Registry/Block #3,085,645

Block #3,085,645

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/9/2019, 4:59:55 PM Β· Difficulty 11.0281 Β· 3,757,291 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d474b2540d2d690d37b7f0bee08387eb3e0feb9067737a476e21f13d9b2792e9
View on Chainz β†—

Difficulty

11.028141

Transactions

1

Size

200 B

Version

2

Bits

0b073444

Nonce

1,743,806,640

Timestamp

3/9/2019, 4:59:55 PM

Confirmations

3,757,291

Merkle Root

6fb6623507c539caf7c0139ab6226e361cb39be70de2cdf1bd09aea163d78c06
Transactions (1)
Coinbase6fb6623507c539…09aea163d78c06
1 in β†’ 1 out8.2100 XPM110 B
AbXwmGxD…4XXYP765
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.

1.249 Γ— 10⁹⁴(95-digit number)
12492370348062908885…88604398720477248160
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
1.249 Γ— 10⁹⁴(95-digit number)
12492370348062908885…88604398720477248159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.498 Γ— 10⁹⁴(95-digit number)
24984740696125817771…77208797440954496319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.996 Γ— 10⁹⁴(95-digit number)
49969481392251635542…54417594881908992639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.993 Γ— 10⁹⁴(95-digit number)
99938962784503271085…08835189763817985279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.998 Γ— 10⁹⁡(96-digit number)
19987792556900654217…17670379527635970559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.997 Γ— 10⁹⁡(96-digit number)
39975585113801308434…35340759055271941119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.995 Γ— 10⁹⁡(96-digit number)
79951170227602616868…70681518110543882239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.599 Γ— 10⁹⁢(97-digit number)
15990234045520523373…41363036221087764479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.198 Γ— 10⁹⁢(97-digit number)
31980468091041046747…82726072442175528959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.396 Γ— 10⁹⁢(97-digit number)
63960936182082093494…65452144884351057919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.279 Γ— 10⁹⁷(98-digit number)
12792187236416418698…30904289768702115839
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 3085645

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 d474b2540d2d690d37b7f0bee08387eb3e0feb9067737a476e21f13d9b2792e9

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 #3,085,645 on Chainz β†—
Circulating Supply:57,987,838 XPMΒ·at block #6,842,935 Β· updates every 60s
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