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Home/Chain Registry/Block #1,426,836

Block #1,426,836

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/24/2016, 10:05:28 PM Β· Difficulty 10.7543 Β· 5,417,030 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d1e08f935fdbff6953b9dd181b77a073a22eb01d1d6c8434c7832d8182afc015
View on Chainz β†—

Difficulty

10.754277

Transactions

1

Size

242 B

Version

2

Bits

0ac11854

Nonce

2,135,802,008

Timestamp

1/24/2016, 10:05:28 PM

Confirmations

5,417,030

Merkle Root

e9c5d42d787835482b7ff0f10b0d34a6c533dd32def12061246889fd603c755b
Transactions (1)
Coinbasee9c5d42d787835…6889fd603c755b
1 in β†’ 2 out8.6300 XPM152 B
AeNeFst2…6pebBnhdALPu3s2c…EJXLjVFh
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.

8.982 Γ— 10⁹⁡(96-digit number)
89829483294906191817…00197869519049563840
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
8.982 Γ— 10⁹⁡(96-digit number)
89829483294906191817…00197869519049563841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.796 Γ— 10⁹⁢(97-digit number)
17965896658981238363…00395739038099127681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.593 Γ— 10⁹⁢(97-digit number)
35931793317962476727…00791478076198255361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.186 Γ— 10⁹⁢(97-digit number)
71863586635924953454…01582956152396510721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.437 Γ— 10⁹⁷(98-digit number)
14372717327184990690…03165912304793021441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.874 Γ— 10⁹⁷(98-digit number)
28745434654369981381…06331824609586042881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.749 Γ— 10⁹⁷(98-digit number)
57490869308739962763…12663649219172085761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.149 Γ— 10⁹⁸(99-digit number)
11498173861747992552…25327298438344171521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.299 Γ— 10⁹⁸(99-digit number)
22996347723495985105…50654596876688343041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.599 Γ— 10⁹⁸(99-digit number)
45992695446991970210…01309193753376686081
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 1426836

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 d1e08f935fdbff6953b9dd181b77a073a22eb01d1d6c8434c7832d8182afc015

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 #1,426,836 on Chainz β†—
Circulating Supply:57,995,298 XPMΒ·at block #6,843,865 Β· updates every 60s
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