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Home/Chain Registry/Block #2,633,499

Block #2,633,499

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/28/2018, 11:33:12 AM Β· Difficulty 11.1936 Β· 4,199,812 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
11f5fe2804a4a560e7e891793173bc71783c5d86aaa2ead9880036ba4f758b56
View on Chainz β†—

Difficulty

11.193630

Transactions

1

Size

199 B

Version

2

Bits

0b3191bc

Nonce

415,952,927

Timestamp

4/28/2018, 11:33:12 AM

Confirmations

4,199,812

Merkle Root

cbc689808c6b429a2b1576948e127751e92043595ac57b37fc091d0792319cbc
Transactions (1)
Coinbasecbc689808c6b42…091d0792319cbc
1 in β†’ 1 out7.9700 XPM110 B
AKpdbLAp…8eGfq81Y
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.

1.013 Γ— 10⁹³(94-digit number)
10130606543115399116…52635517642277321150
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
1.013 Γ— 10⁹³(94-digit number)
10130606543115399116…52635517642277321149
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.026 Γ— 10⁹³(94-digit number)
20261213086230798232…05271035284554642299
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.052 Γ— 10⁹³(94-digit number)
40522426172461596464…10542070569109284599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.104 Γ— 10⁹³(94-digit number)
81044852344923192929…21084141138218569199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.620 Γ— 10⁹⁴(95-digit number)
16208970468984638585…42168282276437138399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.241 Γ— 10⁹⁴(95-digit number)
32417940937969277171…84336564552874276799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.483 Γ— 10⁹⁴(95-digit number)
64835881875938554343…68673129105748553599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.296 Γ— 10⁹⁡(96-digit number)
12967176375187710868…37346258211497107199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.593 Γ— 10⁹⁡(96-digit number)
25934352750375421737…74692516422994214399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.186 Γ— 10⁹⁡(96-digit number)
51868705500750843474…49385032845988428799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.037 Γ— 10⁹⁢(97-digit number)
10373741100150168694…98770065691976857599
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 2633499

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 11f5fe2804a4a560e7e891793173bc71783c5d86aaa2ead9880036ba4f758b56

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 #2,633,499 on Chainz β†—
Circulating Supply:57,910,679 XPMΒ·at block #6,833,310 Β· updates every 60s
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