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Home/Chain Registry/Block #3,503,461

Block #3,503,461

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/7/2020, 5:52:46 AM Β· Difficulty 10.9307 Β· 3,334,769 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
63621b1ebf57853c6a61777836aaf4280a62ebe05f53cd2f03f617c0a212e56f
View on Chainz β†—

Difficulty

10.930720

Transactions

1

Size

201 B

Version

2

Bits

0aee43af

Nonce

1,382,424,360

Timestamp

1/7/2020, 5:52:46 AM

Confirmations

3,334,769

Merkle Root

88d4625e5cf816ddb67ab9512043d9040ce61e229fa6fabe20993a7a757b1d63
Transactions (1)
Coinbase88d4625e5cf816…993a7a757b1d63
1 in β†’ 1 out8.3600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

8.906 Γ— 10⁹⁡(96-digit number)
89069883127139822193…55146045548609772800
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
8.906 Γ— 10⁹⁡(96-digit number)
89069883127139822193…55146045548609772799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.781 Γ— 10⁹⁢(97-digit number)
17813976625427964438…10292091097219545599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.562 Γ— 10⁹⁢(97-digit number)
35627953250855928877…20584182194439091199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.125 Γ— 10⁹⁢(97-digit number)
71255906501711857755…41168364388878182399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.425 Γ— 10⁹⁷(98-digit number)
14251181300342371551…82336728777756364799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.850 Γ— 10⁹⁷(98-digit number)
28502362600684743102…64673457555512729599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.700 Γ— 10⁹⁷(98-digit number)
57004725201369486204…29346915111025459199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.140 Γ— 10⁹⁸(99-digit number)
11400945040273897240…58693830222050918399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.280 Γ— 10⁹⁸(99-digit number)
22801890080547794481…17387660444101836799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.560 Γ— 10⁹⁸(99-digit number)
45603780161095588963…34775320888203673599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.120 Γ— 10⁹⁸(99-digit number)
91207560322191177926…69550641776407347199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 3503461

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 63621b1ebf57853c6a61777836aaf4280a62ebe05f53cd2f03f617c0a212e56f

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 #3,503,461 on Chainz β†—
Circulating Supply:57,950,116 XPMΒ·at block #6,838,229 Β· updates every 60s
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