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Home/Chain Registry/Block #3,166,031

Block #3,166,031

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2019, 8:17:03 AM Β· Difficulty 11.3105 Β· 3,675,863 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ddebb01f76b8d9b0f813a054f04ab52ac8dd670c73be10f86cf11188703f0578
View on Chainz β†—

Difficulty

11.310539

Transactions

1

Size

200 B

Version

2

Bits

0b4f7f79

Nonce

840,374,785

Timestamp

5/3/2019, 8:17:03 AM

Confirmations

3,675,863

Merkle Root

a0fdcccb1e6dcde0280362c4bc8c1d0ff2c71f4a7a94b9ab4c34a7c8ddaf8f0b
Transactions (1)
Coinbasea0fdcccb1e6dcd…34a7c8ddaf8f0b
1 in β†’ 1 out7.8000 XPM110 B
AUMQRepm…tAfKmdW1
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.

9.369 Γ— 10⁹⁴(95-digit number)
93695071191513828816…73990995380223364480
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
9.369 Γ— 10⁹⁴(95-digit number)
93695071191513828816…73990995380223364481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.873 Γ— 10⁹⁡(96-digit number)
18739014238302765763…47981990760446728961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.747 Γ— 10⁹⁡(96-digit number)
37478028476605531526…95963981520893457921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.495 Γ— 10⁹⁡(96-digit number)
74956056953211063053…91927963041786915841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.499 Γ— 10⁹⁢(97-digit number)
14991211390642212610…83855926083573831681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.998 Γ— 10⁹⁢(97-digit number)
29982422781284425221…67711852167147663361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.996 Γ— 10⁹⁢(97-digit number)
59964845562568850442…35423704334295326721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.199 Γ— 10⁹⁷(98-digit number)
11992969112513770088…70847408668590653441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.398 Γ— 10⁹⁷(98-digit number)
23985938225027540177…41694817337181306881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.797 Γ— 10⁹⁷(98-digit number)
47971876450055080354…83389634674362613761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.594 Γ— 10⁹⁷(98-digit number)
95943752900110160708…66779269348725227521
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 3166031

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 ddebb01f76b8d9b0f813a054f04ab52ac8dd670c73be10f86cf11188703f0578

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 #3,166,031 on Chainz β†—
Circulating Supply:57,979,528 XPMΒ·at block #6,841,893 Β· updates every 60s
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