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Home/Chain Registry/Block #2,230,473

Block #2,230,473

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/31/2017, 5:28:03 AM Β· Difficulty 10.9465 Β· 4,595,886 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f2bac1c885f7f92a2cf271d75dce3a03d34427545894f202057c6f7485ab9889
View on Chainz β†—

Difficulty

10.946488

Transactions

2

Size

721 B

Version

2

Bits

0af24d03

Nonce

779,967,585

Timestamp

7/31/2017, 5:28:03 AM

Confirmations

4,595,886

Merkle Root

8021cd53dc1f5010b3d5e2a5138322d92bd0d525d4a4302e4e8321eb3a3bbb9d
Transactions (2)
Coinbase7831dd05971155…ddd20e9a451ebe
1 in β†’ 1 out8.3400 XPM110 B
AW5JAB6g…nZn7yerX
0dc1f13fc7a5f6…87d914ea460439
3 in β†’ 2 out47.3535 XPM522 B
AJwtw6yr…MMqwduyiAG5Tzfx4…MurDeKyc
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.

1.623 Γ— 10⁹²(93-digit number)
16231571154458440917…06955768209877286360
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
1.623 Γ— 10⁹²(93-digit number)
16231571154458440917…06955768209877286359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.246 Γ— 10⁹²(93-digit number)
32463142308916881835…13911536419754572719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.492 Γ— 10⁹²(93-digit number)
64926284617833763670…27823072839509145439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.298 Γ— 10⁹³(94-digit number)
12985256923566752734…55646145679018290879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.597 Γ— 10⁹³(94-digit number)
25970513847133505468…11292291358036581759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.194 Γ— 10⁹³(94-digit number)
51941027694267010936…22584582716073163519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.038 Γ— 10⁹⁴(95-digit number)
10388205538853402187…45169165432146327039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.077 Γ— 10⁹⁴(95-digit number)
20776411077706804374…90338330864292654079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.155 Γ— 10⁹⁴(95-digit number)
41552822155413608748…80676661728585308159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.310 Γ— 10⁹⁴(95-digit number)
83105644310827217497…61353323457170616319
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 2230473

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 f2bac1c885f7f92a2cf271d75dce3a03d34427545894f202057c6f7485ab9889

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 #2,230,473 on Chainz β†—
Circulating Supply:57,855,018 XPMΒ·at block #6,826,358 Β· updates every 60s
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