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Home/Chain Registry/Block #3,086,966

Block #3,086,966

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/10/2019, 2:04:14 PM Β· Difficulty 11.0392 Β· 3,758,145 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e51a3ffce4f8661c57cc88182674e96463005e9e9d8ce18230bc2ecc0f8ec796
View on Chainz β†—

Difficulty

11.039210

Transactions

1

Size

199 B

Version

2

Bits

0b0a09a9

Nonce

82,312,433

Timestamp

3/10/2019, 2:04:14 PM

Confirmations

3,758,145

Merkle Root

f2d6da6ce1ae228e02703aa2ddf050d90ce69852f036ebda5fc96f3842d8ec6d
Transactions (1)
Coinbasef2d6da6ce1ae22…c96f3842d8ec6d
1 in β†’ 1 out8.1900 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)
30380697463906690631…68963270027909743200
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)
30380697463906690631…68963270027909743199
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)
60761394927813381262…37926540055819486399
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)
12152278985562676252…75853080111638972799
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)
24304557971125352505…51706160223277945599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.860 Γ— 10⁹⁴(95-digit number)
48609115942250705010…03412320446555891199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.721 Γ— 10⁹⁴(95-digit number)
97218231884501410020…06824640893111782399
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)
19443646376900282004…13649281786223564799
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)
38887292753800564008…27298563572447129599
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)
77774585507601128016…54597127144894259199
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)
15554917101520225603…09194254289788518399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.110 Γ— 10⁹⁢(97-digit number)
31109834203040451206…18388508579577036799
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 3086966

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 e51a3ffce4f8661c57cc88182674e96463005e9e9d8ce18230bc2ecc0f8ec796

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 #3,086,966 on Chainz β†—
Circulating Supply:58,005,314 XPMΒ·at block #6,845,110 Β· updates every 60s
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