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Home/Chain Registry/Block #2,133,333

Block #2,133,333

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/26/2017, 10:43:40 AM Β· Difficulty 10.9097 Β· 4,711,990 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2ce91a134c11c068ec02291cfd9280acd504ad75a88508f3df01e04eb0ad2125
View on Chainz β†—

Difficulty

10.909717

Transactions

1

Size

200 B

Version

2

Bits

0ae8e338

Nonce

246,027,542

Timestamp

5/26/2017, 10:43:40 AM

Confirmations

4,711,990

Merkle Root

ffd10509f85079fbb7ba25cd18a1889b84907ba1718936469a69d0944dfd11ab
Transactions (1)
Coinbaseffd10509f85079…69d0944dfd11ab
1 in β†’ 1 out8.3900 XPM109 B
AW2bNENJ…HHGssPdZ
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.

1.177 Γ— 10⁹⁢(97-digit number)
11774224412194677906…31351029332050070400
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
1.177 Γ— 10⁹⁢(97-digit number)
11774224412194677906…31351029332050070399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.354 Γ— 10⁹⁢(97-digit number)
23548448824389355812…62702058664100140799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.709 Γ— 10⁹⁢(97-digit number)
47096897648778711625…25404117328200281599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.419 Γ— 10⁹⁢(97-digit number)
94193795297557423250…50808234656400563199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.883 Γ— 10⁹⁷(98-digit number)
18838759059511484650…01616469312801126399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.767 Γ— 10⁹⁷(98-digit number)
37677518119022969300…03232938625602252799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.535 Γ— 10⁹⁷(98-digit number)
75355036238045938600…06465877251204505599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.507 Γ— 10⁹⁸(99-digit number)
15071007247609187720…12931754502409011199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.014 Γ— 10⁹⁸(99-digit number)
30142014495218375440…25863509004818022399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.028 Γ— 10⁹⁸(99-digit number)
60284028990436750880…51727018009636044799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2133333

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 2ce91a134c11c068ec02291cfd9280acd504ad75a88508f3df01e04eb0ad2125

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 #2,133,333 on Chainz β†—
Circulating Supply:58,007,023 XPMΒ·at block #6,845,322 Β· updates every 60s
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