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Home/Chain Registry/Block #2,859,179

Block #2,859,179

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/29/2018, 2:26:26 AM Β· Difficulty 11.6754 Β· 3,979,841 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f32184ba6e372c45f6aa6f3a55f8940a6694fdd74a30056bc6c81aae880920d7
View on Chainz β†—

Difficulty

11.675402

Transactions

1

Size

199 B

Version

2

Bits

0bace727

Nonce

1,500,703,176

Timestamp

9/29/2018, 2:26:26 AM

Confirmations

3,979,841

Merkle Root

da7de9bc1fbf9406730af01bc79dc15add88624eeb0463cf1ae60ee89f0e5fb0
Transactions (1)
Coinbaseda7de9bc1fbf94…e60ee89f0e5fb0
1 in β†’ 1 out7.3200 XPM110 B
AcBzpX5T…tsBkEmey
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.

1.114 Γ— 10⁹²(93-digit number)
11148448485969974741…83022408192712518740
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
1.114 Γ— 10⁹²(93-digit number)
11148448485969974741…83022408192712518739
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.229 Γ— 10⁹²(93-digit number)
22296896971939949482…66044816385425037479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.459 Γ— 10⁹²(93-digit number)
44593793943879898964…32089632770850074959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.918 Γ— 10⁹²(93-digit number)
89187587887759797928…64179265541700149919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.783 Γ— 10⁹³(94-digit number)
17837517577551959585…28358531083400299839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.567 Γ— 10⁹³(94-digit number)
35675035155103919171…56717062166800599679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.135 Γ— 10⁹³(94-digit number)
71350070310207838342…13434124333601199359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.427 Γ— 10⁹⁴(95-digit number)
14270014062041567668…26868248667202398719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.854 Γ— 10⁹⁴(95-digit number)
28540028124083135337…53736497334404797439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.708 Γ— 10⁹⁴(95-digit number)
57080056248166270674…07472994668809594879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.141 Γ— 10⁹⁡(96-digit number)
11416011249633254134…14945989337619189759
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 2859179

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 f32184ba6e372c45f6aa6f3a55f8940a6694fdd74a30056bc6c81aae880920d7

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 #2,859,179 on Chainz β†—
Circulating Supply:57,956,429 XPMΒ·at block #6,839,019 Β· updates every 60s
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