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Home/Chain Registry/Block #2,834,440

Block #2,834,440

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/11/2018, 11:08:38 AM Β· Difficulty 11.7144 Β· 3,997,062 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7ba608bcea58b854d05e15c785243a61e36510fba58e6b42fa729eca3a55c337
View on Chainz β†—

Difficulty

11.714354

Transactions

2

Size

652 B

Version

2

Bits

0bb6dfe3

Nonce

1,933,570,488

Timestamp

9/11/2018, 11:08:38 AM

Confirmations

3,997,062

Merkle Root

0e1391821cceab0a272c15b027b2b7886fde6ed8fb8f0959cd67c7f9faeb43eb
Transactions (2)
Coinbasea46ddff24f41f0…f01b6d2ee25479
1 in β†’ 1 out7.2800 XPM110 B
AZtxQr2F…7grUWrUz
ea80f2821cc491…fcd42366682f29
3 in β†’ 2 out20.8400 XPM453 B
ALx143y6…dHpHRoL3AHNHzk7x…6NrUFzn5
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.

3.084 Γ— 10⁹²(93-digit number)
30845112316825719190…98105193720367640320
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
3.084 Γ— 10⁹²(93-digit number)
30845112316825719190…98105193720367640321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.169 Γ— 10⁹²(93-digit number)
61690224633651438381…96210387440735280641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.233 Γ— 10⁹³(94-digit number)
12338044926730287676…92420774881470561281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.467 Γ— 10⁹³(94-digit number)
24676089853460575352…84841549762941122561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.935 Γ— 10⁹³(94-digit number)
49352179706921150705…69683099525882245121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.870 Γ— 10⁹³(94-digit number)
98704359413842301410…39366199051764490241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.974 Γ— 10⁹⁴(95-digit number)
19740871882768460282…78732398103528980481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.948 Γ— 10⁹⁴(95-digit number)
39481743765536920564…57464796207057960961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.896 Γ— 10⁹⁴(95-digit number)
78963487531073841128…14929592414115921921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.579 Γ— 10⁹⁡(96-digit number)
15792697506214768225…29859184828231843841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.158 Γ— 10⁹⁡(96-digit number)
31585395012429536451…59718369656463687681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
6.317 Γ— 10⁹⁡(96-digit number)
63170790024859072902…19436739312927375361
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2834440

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 7ba608bcea58b854d05e15c785243a61e36510fba58e6b42fa729eca3a55c337

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 #2,834,440 on Chainz β†—
Circulating Supply:57,896,104 XPMΒ·at block #6,831,501 Β· updates every 60s
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