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Home/Chain Registry/Block #1,626,206

Block #1,626,206

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/13/2016, 6:46:16 AM Β· Difficulty 10.5869 Β· 5,200,926 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c942503cb146ecff6d845ff9154eb9e9c5a9eb1966adc7ebe8e377a88c573689
View on Chainz β†—

Difficulty

10.586862

Transactions

1

Size

199 B

Version

2

Bits

0a963c93

Nonce

500,033,338

Timestamp

6/13/2016, 6:46:16 AM

Confirmations

5,200,926

Merkle Root

14e31488127ad37b8a3503fad7d7db499e07acc620f983a17e6bb216ba02da9f
Transactions (1)
Coinbase14e31488127ad3…6bb216ba02da9f
1 in β†’ 1 out8.9100 XPM109 B
Abtd68ky…vF6UmtCC
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.

6.815 Γ— 10⁹⁴(95-digit number)
68157255774056032979…10634779120219175200
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
6.815 Γ— 10⁹⁴(95-digit number)
68157255774056032979…10634779120219175199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.363 Γ— 10⁹⁡(96-digit number)
13631451154811206595…21269558240438350399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.726 Γ— 10⁹⁡(96-digit number)
27262902309622413191…42539116480876700799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.452 Γ— 10⁹⁡(96-digit number)
54525804619244826383…85078232961753401599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.090 Γ— 10⁹⁢(97-digit number)
10905160923848965276…70156465923506803199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.181 Γ— 10⁹⁢(97-digit number)
21810321847697930553…40312931847013606399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.362 Γ— 10⁹⁢(97-digit number)
43620643695395861107…80625863694027212799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.724 Γ— 10⁹⁢(97-digit number)
87241287390791722214…61251727388054425599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.744 Γ— 10⁹⁷(98-digit number)
17448257478158344442…22503454776108851199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.489 Γ— 10⁹⁷(98-digit number)
34896514956316688885…45006909552217702399
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 1626206

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 c942503cb146ecff6d845ff9154eb9e9c5a9eb1966adc7ebe8e377a88c573689

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 #1,626,206 on Chainz β†—
Circulating Supply:57,861,236 XPMΒ·at block #6,827,131 Β· updates every 60s
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