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Home/Chain Registry/Block #1,416,138

Block #1,416,138

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/16/2016, 7:45:37 PM Β· Difficulty 10.7966 Β· 5,426,107 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a49ebca3220a89cb33a87b733ac5b280f986915f08c953caad2f11e5bcf52540
View on Chainz β†—

Difficulty

10.796648

Transactions

1

Size

200 B

Version

2

Bits

0acbf120

Nonce

1,465,125,248

Timestamp

1/16/2016, 7:45:37 PM

Confirmations

5,426,107

Merkle Root

df6312c85f87df6d4ee56aacea9b2db1a346ebffb8758c6f3ddafc43f4a6b3c5
Transactions (1)
Coinbasedf6312c85f87df…dafc43f4a6b3c5
1 in β†’ 1 out8.5700 XPM110 B
AGop1B4Q…XXiRrhF9
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.

1.629 Γ— 10⁹⁴(95-digit number)
16291742667588300501…86384639987019916000
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
1.629 Γ— 10⁹⁴(95-digit number)
16291742667588300501…86384639987019916001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.258 Γ— 10⁹⁴(95-digit number)
32583485335176601002…72769279974039832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.516 Γ— 10⁹⁴(95-digit number)
65166970670353202004…45538559948079664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.303 Γ— 10⁹⁡(96-digit number)
13033394134070640400…91077119896159328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.606 Γ— 10⁹⁡(96-digit number)
26066788268141280801…82154239792318656001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.213 Γ— 10⁹⁡(96-digit number)
52133576536282561603…64308479584637312001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.042 Γ— 10⁹⁢(97-digit number)
10426715307256512320…28616959169274624001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.085 Γ— 10⁹⁢(97-digit number)
20853430614513024641…57233918338549248001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.170 Γ— 10⁹⁢(97-digit number)
41706861229026049282…14467836677098496001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.341 Γ— 10⁹⁢(97-digit number)
83413722458052098565…28935673354196992001
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 1416138

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 a49ebca3220a89cb33a87b733ac5b280f986915f08c953caad2f11e5bcf52540

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 #1,416,138 on Chainz β†—
Circulating Supply:57,982,358 XPMΒ·at block #6,842,244 Β· updates every 60s
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