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Home/Chain Registry/Block #3,020,870

Block #3,020,870

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/22/2019, 5:44:24 PM Β· Difficulty 11.1642 Β· 3,822,431 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e974993d14d3a23b3de6278e82f5dfd917b78d7fab91ef305fd30eb8bc3e7858
View on Chainz β†—

Difficulty

11.164216

Transactions

1

Size

200 B

Version

2

Bits

0b2a0a16

Nonce

957,509,629

Timestamp

1/22/2019, 5:44:24 PM

Confirmations

3,822,431

Merkle Root

a3b1e7c16e8f438c11f6cbbd70ad01565c99517a5b1ba5873506a37a583241e2
Transactions (1)
Coinbasea3b1e7c16e8f43…06a37a583241e2
1 in β†’ 1 out8.0100 XPM110 B
AUhjokok…k5m93PZR
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.

3.474 Γ— 10⁹⁡(96-digit number)
34747422980332007228…78149295880913282560
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
3.474 Γ— 10⁹⁡(96-digit number)
34747422980332007228…78149295880913282561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.949 Γ— 10⁹⁡(96-digit number)
69494845960664014457…56298591761826565121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.389 Γ— 10⁹⁢(97-digit number)
13898969192132802891…12597183523653130241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.779 Γ— 10⁹⁢(97-digit number)
27797938384265605782…25194367047306260481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.559 Γ— 10⁹⁢(97-digit number)
55595876768531211565…50388734094612520961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.111 Γ— 10⁹⁷(98-digit number)
11119175353706242313…00777468189225041921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.223 Γ— 10⁹⁷(98-digit number)
22238350707412484626…01554936378450083841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.447 Γ— 10⁹⁷(98-digit number)
44476701414824969252…03109872756900167681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.895 Γ— 10⁹⁷(98-digit number)
88953402829649938505…06219745513800335361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.779 Γ— 10⁹⁸(99-digit number)
17790680565929987701…12439491027600670721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.558 Γ— 10⁹⁸(99-digit number)
35581361131859975402…24878982055201341441
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 3020870

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 e974993d14d3a23b3de6278e82f5dfd917b78d7fab91ef305fd30eb8bc3e7858

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 #3,020,870 on Chainz β†—
Circulating Supply:57,990,773 XPMΒ·at block #6,843,300 Β· updates every 60s
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