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Home/Chain Registry/Block #3,082,331

Block #3,082,331

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/7/2019, 10:16:38 AM Β· Difficulty 11.0220 Β· 3,758,000 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
99f77bb59a91f6f37bcd39dcf2812b18bf9fd81594e16696b5d647d6f63940bc
View on Chainz β†—

Difficulty

11.021979

Transactions

1

Size

200 B

Version

2

Bits

0b05a070

Nonce

877,310,288

Timestamp

3/7/2019, 10:16:38 AM

Confirmations

3,758,000

Merkle Root

e5d0b1e92f8c5e58b09187e64533975516bfd173a5614ddc1accbc96dc2c47fe
Transactions (1)
Coinbasee5d0b1e92f8c5e…ccbc96dc2c47fe
1 in β†’ 1 out8.2200 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.

8.802 Γ— 10⁹⁡(96-digit number)
88029831604003150110…41183615364728698880
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
8.802 Γ— 10⁹⁡(96-digit number)
88029831604003150110…41183615364728698879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.760 Γ— 10⁹⁢(97-digit number)
17605966320800630022…82367230729457397759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.521 Γ— 10⁹⁢(97-digit number)
35211932641601260044…64734461458914795519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.042 Γ— 10⁹⁢(97-digit number)
70423865283202520088…29468922917829591039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.408 Γ— 10⁹⁷(98-digit number)
14084773056640504017…58937845835659182079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.816 Γ— 10⁹⁷(98-digit number)
28169546113281008035…17875691671318364159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.633 Γ— 10⁹⁷(98-digit number)
56339092226562016070…35751383342636728319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.126 Γ— 10⁹⁸(99-digit number)
11267818445312403214…71502766685273456639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.253 Γ— 10⁹⁸(99-digit number)
22535636890624806428…43005533370546913279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.507 Γ— 10⁹⁸(99-digit number)
45071273781249612856…86011066741093826559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.014 Γ— 10⁹⁸(99-digit number)
90142547562499225713…72022133482187653119
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 3082331

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 99f77bb59a91f6f37bcd39dcf2812b18bf9fd81594e16696b5d647d6f63940bc

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 #3,082,331 on Chainz β†—
Circulating Supply:57,966,968 XPMΒ·at block #6,840,330 Β· updates every 60s
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