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Home/Chain Registry/Block #2,989,104

Block #2,989,104

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/31/2018, 5:01:20 AM Β· Difficulty 11.2680 Β· 3,855,986 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4e180688651f9b92c1ca329aa36f0ec564a6cd119baf0ad33595458efb1e9822
View on Chainz β†—

Difficulty

11.267959

Transactions

1

Size

200 B

Version

2

Bits

0b4498f4

Nonce

346,670,515

Timestamp

12/31/2018, 5:01:20 AM

Confirmations

3,855,986

Merkle Root

6f7a0217b45ae615749a7b9ab2defc647223e6245e8015f6f7ed478cabb1c8bc
Transactions (1)
Coinbase6f7a0217b45ae6…ed478cabb1c8bc
1 in β†’ 1 out7.8600 XPM109 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.

7.182 Γ— 10⁹⁢(97-digit number)
71824509560366218408…42056205222368645120
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
7.182 Γ— 10⁹⁢(97-digit number)
71824509560366218408…42056205222368645119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.436 Γ— 10⁹⁷(98-digit number)
14364901912073243681…84112410444737290239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.872 Γ— 10⁹⁷(98-digit number)
28729803824146487363…68224820889474580479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.745 Γ— 10⁹⁷(98-digit number)
57459607648292974726…36449641778949160959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.149 Γ— 10⁹⁸(99-digit number)
11491921529658594945…72899283557898321919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.298 Γ— 10⁹⁸(99-digit number)
22983843059317189890…45798567115796643839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.596 Γ— 10⁹⁸(99-digit number)
45967686118634379781…91597134231593287679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.193 Γ— 10⁹⁸(99-digit number)
91935372237268759562…83194268463186575359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.838 Γ— 10⁹⁹(100-digit number)
18387074447453751912…66388536926373150719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.677 Γ— 10⁹⁹(100-digit number)
36774148894907503825…32777073852746301439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.354 Γ— 10⁹⁹(100-digit number)
73548297789815007650…65554147705492602879
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 2989104

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 4e180688651f9b92c1ca329aa36f0ec564a6cd119baf0ad33595458efb1e9822

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 #2,989,104 on Chainz β†—
Circulating Supply:58,005,148 XPMΒ·at block #6,845,089 Β· updates every 60s
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