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Home/Chain Registry/Block #2,526,454

Block #2,526,454

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/18/2018, 4:32:51 AM Β· Difficulty 10.9839 Β· 4,317,282 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1e0188d41ef278daad48cfbcf07a55eb19b76d3098b08609d46fc70a2818c2a2
View on Chainz β†—

Difficulty

10.983877

Transactions

1

Size

199 B

Version

2

Bits

0afbdf64

Nonce

1,832,675,274

Timestamp

2/18/2018, 4:32:51 AM

Confirmations

4,317,282

Merkle Root

9aaba2517ee9ccd0584444ddb9045b3ab2d714405ae3c14a4b7364e300ac7092
Transactions (1)
Coinbase9aaba2517ee9cc…7364e300ac7092
1 in β†’ 1 out8.2800 XPM109 B
AV4FwyFj…AXJND6Bo
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.

1.435 Γ— 10⁹⁡(96-digit number)
14356309665410760087…79433317542100035840
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
1.435 Γ— 10⁹⁡(96-digit number)
14356309665410760087…79433317542100035841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.871 Γ— 10⁹⁡(96-digit number)
28712619330821520174…58866635084200071681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.742 Γ— 10⁹⁡(96-digit number)
57425238661643040348…17733270168400143361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.148 Γ— 10⁹⁢(97-digit number)
11485047732328608069…35466540336800286721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.297 Γ— 10⁹⁢(97-digit number)
22970095464657216139…70933080673600573441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.594 Γ— 10⁹⁢(97-digit number)
45940190929314432278…41866161347201146881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.188 Γ— 10⁹⁢(97-digit number)
91880381858628864556…83732322694402293761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.837 Γ— 10⁹⁷(98-digit number)
18376076371725772911…67464645388804587521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.675 Γ— 10⁹⁷(98-digit number)
36752152743451545822…34929290777609175041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.350 Γ— 10⁹⁷(98-digit number)
73504305486903091645…69858581555218350081
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 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
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 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 2526454

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 1e0188d41ef278daad48cfbcf07a55eb19b76d3098b08609d46fc70a2818c2a2

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 #2,526,454 on Chainz β†—
Circulating Supply:57,994,256 XPMΒ·at block #6,843,735 Β· updates every 60s
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