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Home/Chain Registry/Block #2,796,048

Block #2,796,048

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/16/2018, 4:00:14 AM Β· Difficulty 11.6817 Β· 4,040,824 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bb2638add39220d67c785d6195edba566c651e551e1c35e9c617dc20672cd8e1
View on Chainz β†—

Difficulty

11.681685

Transactions

1

Size

200 B

Version

2

Bits

0bae82e4

Nonce

138,135,273

Timestamp

8/16/2018, 4:00:14 AM

Confirmations

4,040,824

Merkle Root

87892cc01defecf072f1d0d9c3e37d5377596b4439e18416638a976744e6ea63
Transactions (1)
Coinbase87892cc01defec…8a976744e6ea63
1 in β†’ 1 out7.3200 XPM109 B
AZtxQr2F…7grUWrUz
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.

4.308 Γ— 10⁹⁢(97-digit number)
43088958423325500468…02734655930217111040
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
4.308 Γ— 10⁹⁢(97-digit number)
43088958423325500468…02734655930217111039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.617 Γ— 10⁹⁢(97-digit number)
86177916846651000937…05469311860434222079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.723 Γ— 10⁹⁷(98-digit number)
17235583369330200187…10938623720868444159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.447 Γ— 10⁹⁷(98-digit number)
34471166738660400374…21877247441736888319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.894 Γ— 10⁹⁷(98-digit number)
68942333477320800749…43754494883473776639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.378 Γ— 10⁹⁸(99-digit number)
13788466695464160149…87508989766947553279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.757 Γ— 10⁹⁸(99-digit number)
27576933390928320299…75017979533895106559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.515 Γ— 10⁹⁸(99-digit number)
55153866781856640599…50035959067790213119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.103 Γ— 10⁹⁹(100-digit number)
11030773356371328119…00071918135580426239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.206 Γ— 10⁹⁹(100-digit number)
22061546712742656239…00143836271160852479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.412 Γ— 10⁹⁹(100-digit number)
44123093425485312479…00287672542321704959
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 2796048

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 bb2638add39220d67c785d6195edba566c651e551e1c35e9c617dc20672cd8e1

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 #2,796,048 on Chainz β†—
Circulating Supply:57,939,266 XPMΒ·at block #6,836,871 Β· updates every 60s
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