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Home/Chain Registry/Block #1,408,659

Block #1,408,659

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/11/2016, 11:25:46 AM Β· Difficulty 10.8051 Β· 5,436,551 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1d6d6b6be926ba7f443092ba394f27fa4cc0fb908b223df8b2acf6acb617be76
View on Chainz β†—

Difficulty

10.805084

Transactions

1

Size

199 B

Version

2

Bits

0ace19f9

Nonce

2,142,474,152

Timestamp

1/11/2016, 11:25:46 AM

Confirmations

5,436,551

Merkle Root

1be5a9135b55f7cf3629e2976b8b4d89313b1aba4ca214e712acc6df5f245041
Transactions (1)
Coinbase1be5a9135b55f7…acc6df5f245041
1 in β†’ 1 out8.5500 XPM109 B
AHcqodYD…UuqYjUun
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.

2.943 Γ— 10⁹⁡(96-digit number)
29433991276309388169…25210929110337217280
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
2.943 Γ— 10⁹⁡(96-digit number)
29433991276309388169…25210929110337217279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.886 Γ— 10⁹⁡(96-digit number)
58867982552618776338…50421858220674434559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.177 Γ— 10⁹⁢(97-digit number)
11773596510523755267…00843716441348869119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.354 Γ— 10⁹⁢(97-digit number)
23547193021047510535…01687432882697738239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.709 Γ— 10⁹⁢(97-digit number)
47094386042095021070…03374865765395476479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.418 Γ— 10⁹⁢(97-digit number)
94188772084190042141…06749731530790952959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.883 Γ— 10⁹⁷(98-digit number)
18837754416838008428…13499463061581905919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.767 Γ— 10⁹⁷(98-digit number)
37675508833676016856…26998926123163811839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.535 Γ— 10⁹⁷(98-digit number)
75351017667352033713…53997852246327623679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.507 Γ— 10⁹⁸(99-digit number)
15070203533470406742…07995704492655247359
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 1408659

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 1d6d6b6be926ba7f443092ba394f27fa4cc0fb908b223df8b2acf6acb617be76

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 #1,408,659 on Chainz β†—
Circulating Supply:58,006,112 XPMΒ·at block #6,845,209 Β· updates every 60s
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