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Home/Chain Registry/Block #2,516,413

Block #2,516,413

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/12/2018, 12:49:23 AM Β· Difficulty 10.9793 Β· 4,326,756 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5970b77f1bd49a6fd6cc38710f76397ce2f198a75656f28033c7dea39c6348d3
View on Chainz β†—

Difficulty

10.979281

Transactions

1

Size

199 B

Version

2

Bits

0afab229

Nonce

1,036,753,919

Timestamp

2/12/2018, 12:49:23 AM

Confirmations

4,326,756

Merkle Root

323fc2fb5088143969cfdb01e9217a361771660967e63b621a503df1e5084775
Transactions (1)
Coinbase323fc2fb508814…503df1e5084775
1 in β†’ 1 out8.2800 XPM109 B
AREYLPQr…4cLX9Rhd
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.

1.096 Γ— 10⁹⁴(95-digit number)
10966980773961940056…71596751317234877200
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
1.096 Γ— 10⁹⁴(95-digit number)
10966980773961940056…71596751317234877199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.193 Γ— 10⁹⁴(95-digit number)
21933961547923880112…43193502634469754399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.386 Γ— 10⁹⁴(95-digit number)
43867923095847760224…86387005268939508799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.773 Γ— 10⁹⁴(95-digit number)
87735846191695520449…72774010537879017599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.754 Γ— 10⁹⁡(96-digit number)
17547169238339104089…45548021075758035199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.509 Γ— 10⁹⁡(96-digit number)
35094338476678208179…91096042151516070399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.018 Γ— 10⁹⁡(96-digit number)
70188676953356416359…82192084303032140799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.403 Γ— 10⁹⁢(97-digit number)
14037735390671283271…64384168606064281599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.807 Γ— 10⁹⁢(97-digit number)
28075470781342566543…28768337212128563199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.615 Γ— 10⁹⁢(97-digit number)
56150941562685133087…57536674424257126399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.123 Γ— 10⁹⁷(98-digit number)
11230188312537026617…15073348848514252799
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 2516413

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 5970b77f1bd49a6fd6cc38710f76397ce2f198a75656f28033c7dea39c6348d3

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 #2,516,413 on Chainz β†—
Circulating Supply:57,989,718 XPMΒ·at block #6,843,168 Β· updates every 60s
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