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Home/Chain Registry/Block #2,528,600

Block #2,528,600

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/19/2018, 12:26:17 PM Β· Difficulty 10.9847 Β· 4,312,855 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
704f15bb0c8ba9b06a3b34472c70e0a28367272947727bdf2e114a25c2c5837a
View on Chainz β†—

Difficulty

10.984655

Transactions

1

Size

199 B

Version

2

Bits

0afc1261

Nonce

658,373,917

Timestamp

2/19/2018, 12:26:17 PM

Confirmations

4,312,855

Merkle Root

c610e52bc3b6440ed6127d447a4145a69f0b2a2b99b5818b5d00bb965fd62131
Transactions (1)
Coinbasec610e52bc3b644…00bb965fd62131
1 in β†’ 1 out8.2700 XPM109 B
ANjFukbt…tesdFxQ8
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.

3.160 Γ— 10⁹⁡(96-digit number)
31600788931649746289…60088830145198588800
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
3.160 Γ— 10⁹⁡(96-digit number)
31600788931649746289…60088830145198588801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.320 Γ— 10⁹⁡(96-digit number)
63201577863299492579…20177660290397177601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.264 Γ— 10⁹⁢(97-digit number)
12640315572659898515…40355320580794355201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.528 Γ— 10⁹⁢(97-digit number)
25280631145319797031…80710641161588710401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.056 Γ— 10⁹⁢(97-digit number)
50561262290639594063…61421282323177420801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.011 Γ— 10⁹⁷(98-digit number)
10112252458127918812…22842564646354841601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.022 Γ— 10⁹⁷(98-digit number)
20224504916255837625…45685129292709683201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.044 Γ— 10⁹⁷(98-digit number)
40449009832511675250…91370258585419366401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.089 Γ— 10⁹⁷(98-digit number)
80898019665023350501…82740517170838732801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.617 Γ— 10⁹⁸(99-digit number)
16179603933004670100…65481034341677465601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.235 Γ— 10⁹⁸(99-digit number)
32359207866009340200…30962068683354931201
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 2528600

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 704f15bb0c8ba9b06a3b34472c70e0a28367272947727bdf2e114a25c2c5837a

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 #2,528,600 on Chainz β†—
Circulating Supply:57,976,020 XPMΒ·at block #6,841,454 Β· updates every 60s
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