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Home/Chain Registry/Block #2,116,663

Block #2,116,663

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/15/2017, 1:12:36 AM Β· Difficulty 10.9044 Β· 4,728,247 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
748486ead963d93f396576023eeb1977bd061eb14eb7201b7aa4e564ee8ad3ea
View on Chainz β†—

Difficulty

10.904410

Transactions

1

Size

201 B

Version

2

Bits

0ae78765

Nonce

211,718,479

Timestamp

5/15/2017, 1:12:36 AM

Confirmations

4,728,247

Merkle Root

e7d588e35dbd8397f56f79e6749c8b187e9f5ac2246a4ff71d6014c90515cf24
Transactions (1)
Coinbasee7d588e35dbd83…6014c90515cf24
1 in β†’ 1 out8.4000 XPM110 B
AME53Nc8…JKhz6QKT
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.

1.036 Γ— 10⁹⁷(98-digit number)
10364009583527919278…27784418266943180800
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
1.036 Γ— 10⁹⁷(98-digit number)
10364009583527919278…27784418266943180799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.072 Γ— 10⁹⁷(98-digit number)
20728019167055838556…55568836533886361599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.145 Γ— 10⁹⁷(98-digit number)
41456038334111677112…11137673067772723199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.291 Γ— 10⁹⁷(98-digit number)
82912076668223354224…22275346135545446399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.658 Γ— 10⁹⁸(99-digit number)
16582415333644670844…44550692271090892799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.316 Γ— 10⁹⁸(99-digit number)
33164830667289341689…89101384542181785599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.632 Γ— 10⁹⁸(99-digit number)
66329661334578683379…78202769084363571199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.326 Γ— 10⁹⁹(100-digit number)
13265932266915736675…56405538168727142399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.653 Γ— 10⁹⁹(100-digit number)
26531864533831473351…12811076337454284799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.306 Γ— 10⁹⁹(100-digit number)
53063729067662946703…25622152674908569599
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 2116663

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 748486ead963d93f396576023eeb1977bd061eb14eb7201b7aa4e564ee8ad3ea

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 #2,116,663 on Chainz β†—
Circulating Supply:58,003,695 XPMΒ·at block #6,844,909 Β· updates every 60s
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