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Home/Chain Registry/Block #3,077,812

Block #3,077,812

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/4/2019, 8:29:48 AM Β· Difficulty 11.0045 Β· 3,764,982 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d9a0365db89a16d47eeedb883da49499e7ba5716369cb32be4a68bf617fdc0f4
View on Chainz β†—

Difficulty

11.004508

Transactions

1

Size

200 B

Version

2

Bits

0b012778

Nonce

74,691,945

Timestamp

3/4/2019, 8:29:48 AM

Confirmations

3,764,982

Merkle Root

47398a813ac782caa33c04d1d968fa08493b002349c15a1faced48060e9f88f1
Transactions (1)
Coinbase47398a813ac782…ed48060e9f88f1
1 in β†’ 1 out8.2400 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.

3.038 Γ— 10⁹³(94-digit number)
30381738804904253513…38328825388752375500
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
3.038 Γ— 10⁹³(94-digit number)
30381738804904253513…38328825388752375499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.076 Γ— 10⁹³(94-digit number)
60763477609808507026…76657650777504750999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.215 Γ— 10⁹⁴(95-digit number)
12152695521961701405…53315301555009501999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.430 Γ— 10⁹⁴(95-digit number)
24305391043923402810…06630603110019003999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.861 Γ— 10⁹⁴(95-digit number)
48610782087846805621…13261206220038007999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.722 Γ— 10⁹⁴(95-digit number)
97221564175693611242…26522412440076015999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.944 Γ— 10⁹⁡(96-digit number)
19444312835138722248…53044824880152031999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.888 Γ— 10⁹⁡(96-digit number)
38888625670277444496…06089649760304063999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.777 Γ— 10⁹⁡(96-digit number)
77777251340554888993…12179299520608127999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.555 Γ— 10⁹⁢(97-digit number)
15555450268110977798…24358599041216255999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.111 Γ— 10⁹⁢(97-digit number)
31110900536221955597…48717198082432511999
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 3077812

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 d9a0365db89a16d47eeedb883da49499e7ba5716369cb32be4a68bf617fdc0f4

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 #3,077,812 on Chainz β†—
Circulating Supply:57,986,692 XPMΒ·at block #6,842,793 Β· updates every 60s
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