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Home/Chain Registry/Block #2,088,141

Block #2,088,141

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/26/2017, 3:34:15 AM Β· Difficulty 10.8752 Β· 4,756,718 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5dbdddd5405c4c23fd0b21bcd2bca3cf1b4e145b9c0ce55b105faf2a17b77392
View on Chainz β†—

Difficulty

10.875206

Transactions

1

Size

199 B

Version

2

Bits

0ae00d78

Nonce

25,270,398

Timestamp

4/26/2017, 3:34:15 AM

Confirmations

4,756,718

Merkle Root

a7e0e9eb448bbaf66e0f85a92a2ee857656b04880fca2257ddc65f600931c659
Transactions (1)
Coinbasea7e0e9eb448bba…c65f600931c659
1 in β†’ 1 out8.4400 XPM109 B
ALsVGjNK…Paq3cSHs
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.

3.547 Γ— 10⁹³(94-digit number)
35474316094535016242…51968972024599540560
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
3.547 Γ— 10⁹³(94-digit number)
35474316094535016242…51968972024599540561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.094 Γ— 10⁹³(94-digit number)
70948632189070032484…03937944049199081121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.418 Γ— 10⁹⁴(95-digit number)
14189726437814006496…07875888098398162241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.837 Γ— 10⁹⁴(95-digit number)
28379452875628012993…15751776196796324481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.675 Γ— 10⁹⁴(95-digit number)
56758905751256025987…31503552393592648961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.135 Γ— 10⁹⁡(96-digit number)
11351781150251205197…63007104787185297921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.270 Γ— 10⁹⁡(96-digit number)
22703562300502410394…26014209574370595841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.540 Γ— 10⁹⁡(96-digit number)
45407124601004820789…52028419148741191681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.081 Γ— 10⁹⁡(96-digit number)
90814249202009641579…04056838297482383361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.816 Γ— 10⁹⁢(97-digit number)
18162849840401928315…08113676594964766721
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 2088141

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 5dbdddd5405c4c23fd0b21bcd2bca3cf1b4e145b9c0ce55b105faf2a17b77392

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 #2,088,141 on Chainz β†—
Circulating Supply:58,003,284 XPMΒ·at block #6,844,858 Β· updates every 60s
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