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Home/Chain Registry/Block #3,166,028

Block #3,166,028

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/3/2019, 8:14:11 AM Β· Difficulty 11.3105 Β· 3,677,430 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
148b6a774f6f8bb1fdf1df64cae6769cf2db6459781b825e9a42fa32cb4aa72f
View on Chainz β†—

Difficulty

11.310548

Transactions

1

Size

200 B

Version

2

Bits

0b4f8011

Nonce

1,160,011,620

Timestamp

5/3/2019, 8:14:11 AM

Confirmations

3,677,430

Merkle Root

ded9c4db622daab9057e7abc95b591a41b22020c4001e6e5fc6cc163c7937e41
Transactions (1)
Coinbaseded9c4db622daa…6cc163c7937e41
1 in β†’ 1 out7.8000 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.

1.434 Γ— 10⁹⁴(95-digit number)
14345060358149595939…55697335737259103360
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
1.434 Γ— 10⁹⁴(95-digit number)
14345060358149595939…55697335737259103359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.869 Γ— 10⁹⁴(95-digit number)
28690120716299191879…11394671474518206719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.738 Γ— 10⁹⁴(95-digit number)
57380241432598383758…22789342949036413439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.147 Γ— 10⁹⁡(96-digit number)
11476048286519676751…45578685898072826879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.295 Γ— 10⁹⁡(96-digit number)
22952096573039353503…91157371796145653759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.590 Γ— 10⁹⁡(96-digit number)
45904193146078707006…82314743592291307519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.180 Γ— 10⁹⁡(96-digit number)
91808386292157414012…64629487184582615039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.836 Γ— 10⁹⁢(97-digit number)
18361677258431482802…29258974369165230079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.672 Γ— 10⁹⁢(97-digit number)
36723354516862965605…58517948738330460159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.344 Γ— 10⁹⁢(97-digit number)
73446709033725931210…17035897476660920319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.468 Γ— 10⁹⁷(98-digit number)
14689341806745186242…34071794953321840639
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 3166028

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 148b6a774f6f8bb1fdf1df64cae6769cf2db6459781b825e9a42fa32cb4aa72f

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 #3,166,028 on Chainz β†—
Circulating Supply:57,992,032 XPMΒ·at block #6,843,457 Β· updates every 60s
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