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Home/Chain Registry/Block #2,784,836

Block #2,784,836

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/8/2018, 12:20:06 PM Β· Difficulty 11.6690 Β· 4,042,150 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4b3d3604add9e5aa4f7b0858e69748749f0c02cd3359ff569cb7919ef51b3be6
View on Chainz β†—

Difficulty

11.668997

Transactions

1

Size

199 B

Version

2

Bits

0bab4361

Nonce

1,086,929,512

Timestamp

8/8/2018, 12:20:06 PM

Confirmations

4,042,150

Merkle Root

bb6752d5cc30880126bc1721a55c093aa91df6214b97793e71f46eccb2ea6622
Transactions (1)
Coinbasebb6752d5cc3088…f46eccb2ea6622
1 in β†’ 1 out7.3300 XPM110 B
AGvLSdZ7…ZEz7RCHe
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.

9.062 Γ— 10⁹¹(92-digit number)
90623984406598969278…88555374994438298720
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
9.062 Γ— 10⁹¹(92-digit number)
90623984406598969278…88555374994438298719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.812 Γ— 10⁹²(93-digit number)
18124796881319793855…77110749988876597439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.624 Γ— 10⁹²(93-digit number)
36249593762639587711…54221499977753194879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.249 Γ— 10⁹²(93-digit number)
72499187525279175422…08442999955506389759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.449 Γ— 10⁹³(94-digit number)
14499837505055835084…16885999911012779519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.899 Γ— 10⁹³(94-digit number)
28999675010111670169…33771999822025559039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.799 Γ— 10⁹³(94-digit number)
57999350020223340338…67543999644051118079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.159 Γ— 10⁹⁴(95-digit number)
11599870004044668067…35087999288102236159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.319 Γ— 10⁹⁴(95-digit number)
23199740008089336135…70175998576204472319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.639 Γ— 10⁹⁴(95-digit number)
46399480016178672270…40351997152408944639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.279 Γ— 10⁹⁴(95-digit number)
92798960032357344541…80703994304817889279
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 2784836

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 4b3d3604add9e5aa4f7b0858e69748749f0c02cd3359ff569cb7919ef51b3be6

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 #2,784,836 on Chainz β†—
Circulating Supply:57,860,063 XPMΒ·at block #6,826,985 Β· updates every 60s
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