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Home/Chain Registry/Block #2,834,215

Block #2,834,215

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/11/2018, 7:12:21 AM Β· Difficulty 11.7152 Β· 3,999,362 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0d222129b8013394c258f0d9013e763a46a1a4b994d32ef29913bfd523bec9f1
View on Chainz β†—

Difficulty

11.715151

Transactions

1

Size

200 B

Version

2

Bits

0bb71427

Nonce

119,016,696

Timestamp

9/11/2018, 7:12:21 AM

Confirmations

3,999,362

Merkle Root

6e84628ba85be0a586ccf3269b11442b751f032bbcf40fa2eff406fb6437d199
Transactions (1)
Coinbase6e84628ba85be0…f406fb6437d199
1 in β†’ 1 out7.2700 XPM110 B
ASuwknNA…NcUZngWG
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.

1.740 Γ— 10⁹⁡(96-digit number)
17405208579707511898…74884544487643207460
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
1.740 Γ— 10⁹⁡(96-digit number)
17405208579707511898…74884544487643207461
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.481 Γ— 10⁹⁡(96-digit number)
34810417159415023797…49769088975286414921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.962 Γ— 10⁹⁡(96-digit number)
69620834318830047595…99538177950572829841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.392 Γ— 10⁹⁢(97-digit number)
13924166863766009519…99076355901145659681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.784 Γ— 10⁹⁢(97-digit number)
27848333727532019038…98152711802291319361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.569 Γ— 10⁹⁢(97-digit number)
55696667455064038076…96305423604582638721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.113 Γ— 10⁹⁷(98-digit number)
11139333491012807615…92610847209165277441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.227 Γ— 10⁹⁷(98-digit number)
22278666982025615230…85221694418330554881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.455 Γ— 10⁹⁷(98-digit number)
44557333964051230461…70443388836661109761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.911 Γ— 10⁹⁷(98-digit number)
89114667928102460922…40886777673322219521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.782 Γ— 10⁹⁸(99-digit number)
17822933585620492184…81773555346644439041
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 2834215

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 0d222129b8013394c258f0d9013e763a46a1a4b994d32ef29913bfd523bec9f1

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 #2,834,215 on Chainz β†—
Circulating Supply:57,912,820 XPMΒ·at block #6,833,576 Β· updates every 60s
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