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Home/Chain Registry/Block #2,110,350

Block #2,110,350

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/10/2017, 5:24:31 PM Β· Difficulty 10.9026 Β· 4,727,949 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2350cb77e4d5c2d4e629321e4e4ed985e65b288be4d58c821c13a9966e927fdb
View on Chainz β†—

Difficulty

10.902573

Transactions

1

Size

199 B

Version

2

Bits

0ae70f0a

Nonce

325,738,107

Timestamp

5/10/2017, 5:24:31 PM

Confirmations

4,727,949

Merkle Root

a0b51d9ba54a729a8fa658f541be90f1eb3ad2e74cc703a79aa0025b00520c1b
Transactions (1)
Coinbasea0b51d9ba54a72…a0025b00520c1b
1 in β†’ 1 out8.4000 XPM109 B
AeYaBRxu…xc5e6CbX
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.

9.854 Γ— 10⁹⁴(95-digit number)
98540143364675242041…65624748685333869120
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
9.854 Γ— 10⁹⁴(95-digit number)
98540143364675242041…65624748685333869119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.970 Γ— 10⁹⁡(96-digit number)
19708028672935048408…31249497370667738239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.941 Γ— 10⁹⁡(96-digit number)
39416057345870096816…62498994741335476479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.883 Γ— 10⁹⁡(96-digit number)
78832114691740193633…24997989482670952959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.576 Γ— 10⁹⁢(97-digit number)
15766422938348038726…49995978965341905919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.153 Γ— 10⁹⁢(97-digit number)
31532845876696077453…99991957930683811839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.306 Γ— 10⁹⁢(97-digit number)
63065691753392154906…99983915861367623679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.261 Γ— 10⁹⁷(98-digit number)
12613138350678430981…99967831722735247359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.522 Γ— 10⁹⁷(98-digit number)
25226276701356861962…99935663445470494719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.045 Γ— 10⁹⁷(98-digit number)
50452553402713723925…99871326890940989439
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 2110350

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 2350cb77e4d5c2d4e629321e4e4ed985e65b288be4d58c821c13a9966e927fdb

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 #2,110,350 on Chainz β†—
Circulating Supply:57,950,668 XPMΒ·at block #6,838,298 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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