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Home/Chain Registry/Block #2,458,358

Block #2,458,358

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/5/2018, 6:20:27 AM Β· Difficulty 10.9545 Β· 4,382,966 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
71a042a52a4841da484b5903c16aaf25ba22f873ffdcf46000d46abbfb8a3a18
View on Chainz β†—

Difficulty

10.954465

Transactions

2

Size

571 B

Version

2

Bits

0af457ce

Nonce

456,774,819

Timestamp

1/5/2018, 6:20:27 AM

Confirmations

4,382,966

Merkle Root

46c6ba398c9641b257c5856564e5769466af0bd26dfedd617da051e8947158ea
Transactions (2)
Coinbase4ce51e0f74058e…23d071644f8309
1 in β†’ 1 out8.3300 XPM109 B
AJHkLY3k…91pW89Lg
92c0a75ece8e7d…e0d614f61c299d
2 in β†’ 2 out2278.4900 XPM373 B
AXwsmPPr…6VMrFrtMAHXxV7gh…oVTkZrCQ
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.

3.547 Γ— 10⁹²(93-digit number)
35479997696811802933…55760093071455448400
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
3.547 Γ— 10⁹²(93-digit number)
35479997696811802933…55760093071455448399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.095 Γ— 10⁹²(93-digit number)
70959995393623605866…11520186142910896799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.419 Γ— 10⁹³(94-digit number)
14191999078724721173…23040372285821793599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.838 Γ— 10⁹³(94-digit number)
28383998157449442346…46080744571643587199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.676 Γ— 10⁹³(94-digit number)
56767996314898884693…92161489143287174399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.135 Γ— 10⁹⁴(95-digit number)
11353599262979776938…84322978286574348799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.270 Γ— 10⁹⁴(95-digit number)
22707198525959553877…68645956573148697599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.541 Γ— 10⁹⁴(95-digit number)
45414397051919107754…37291913146297395199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.082 Γ— 10⁹⁴(95-digit number)
90828794103838215509…74583826292594790399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.816 Γ— 10⁹⁡(96-digit number)
18165758820767643101…49167652585189580799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2458358

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 71a042a52a4841da484b5903c16aaf25ba22f873ffdcf46000d46abbfb8a3a18

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 #2,458,358 on Chainz β†—
Circulating Supply:57,974,956 XPMΒ·at block #6,841,323 Β· updates every 60s
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