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Home/Chain Registry/Block #2,833,161

Block #2,833,161

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2018, 1:40:52 PM Β· Difficulty 11.7148 Β· 4,010,150 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f34afc691716adc78df6eeadcb9c516d531f65e88fae9e58f9d5d80c6edd117e
View on Chainz β†—

Difficulty

11.714839

Transactions

1

Size

199 B

Version

2

Bits

0bb6ffb6

Nonce

949,630,009

Timestamp

9/10/2018, 1:40:52 PM

Confirmations

4,010,150

Merkle Root

da6d65d39efe48b1821950bf9f6fe13214f5d6513ec350a772eceb6a3d01153f
Transactions (1)
Coinbaseda6d65d39efe48…eceb6a3d01153f
1 in β†’ 1 out7.2700 XPM110 B
AV8pjSFu…wM6KoJxr
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.

8.956 Γ— 10⁹²(93-digit number)
89560977938926651559…04493091486329174460
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
8.956 Γ— 10⁹²(93-digit number)
89560977938926651559…04493091486329174459
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.791 Γ— 10⁹³(94-digit number)
17912195587785330311…08986182972658348919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.582 Γ— 10⁹³(94-digit number)
35824391175570660623…17972365945316697839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.164 Γ— 10⁹³(94-digit number)
71648782351141321247…35944731890633395679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.432 Γ— 10⁹⁴(95-digit number)
14329756470228264249…71889463781266791359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.865 Γ— 10⁹⁴(95-digit number)
28659512940456528499…43778927562533582719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.731 Γ— 10⁹⁴(95-digit number)
57319025880913056998…87557855125067165439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.146 Γ— 10⁹⁡(96-digit number)
11463805176182611399…75115710250134330879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.292 Γ— 10⁹⁡(96-digit number)
22927610352365222799…50231420500268661759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.585 Γ— 10⁹⁡(96-digit number)
45855220704730445598…00462841000537323519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.171 Γ— 10⁹⁡(96-digit number)
91710441409460891197…00925682001074647039
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 2833161

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 f34afc691716adc78df6eeadcb9c516d531f65e88fae9e58f9d5d80c6edd117e

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 #2,833,161 on Chainz β†—
Circulating Supply:57,990,855 XPMΒ·at block #6,843,310 Β· updates every 60s
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