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Home/Chain Registry/Block #3,506,691

Block #3,506,691

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/9/2020, 11:58:09 AM Β· Difficulty 10.9306 Β· 3,337,995 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8506fdd7896b6cb2e8d47a4ee1c8e13a31b297950eb906c796b3c06bbfc08e5d
View on Chainz β†—

Difficulty

10.930615

Transactions

2

Size

391 B

Version

2

Bits

0aee3cc8

Nonce

152,894,148

Timestamp

1/9/2020, 11:58:09 AM

Confirmations

3,337,995

Merkle Root

30ff79b2fbb33ead37dd87c1018012569a984cdea966ee29262f9b2a57187d5c
Transactions (2)
Coinbase1bfe2f0f13e242…039c034a3dd8e2
1 in β†’ 1 out8.3700 XPM110 B
ASiq2qtK…VMhmk7yL
6c40afc159ed6c…5b45c84b6e74f4
1 in β†’ 1 out24.9920 XPM191 B
ALcTQaSP…1C5Yf2Zi
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.

2.955 Γ— 10⁹⁡(96-digit number)
29550265165148585921…32443306459570370560
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
2.955 Γ— 10⁹⁡(96-digit number)
29550265165148585921…32443306459570370559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.910 Γ— 10⁹⁡(96-digit number)
59100530330297171843…64886612919140741119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.182 Γ— 10⁹⁢(97-digit number)
11820106066059434368…29773225838281482239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.364 Γ— 10⁹⁢(97-digit number)
23640212132118868737…59546451676562964479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.728 Γ— 10⁹⁢(97-digit number)
47280424264237737474…19092903353125928959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.456 Γ— 10⁹⁢(97-digit number)
94560848528475474949…38185806706251857919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.891 Γ— 10⁹⁷(98-digit number)
18912169705695094989…76371613412503715839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.782 Γ— 10⁹⁷(98-digit number)
37824339411390189979…52743226825007431679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.564 Γ— 10⁹⁷(98-digit number)
75648678822780379959…05486453650014863359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.512 Γ— 10⁹⁸(99-digit number)
15129735764556075991…10972907300029726719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.025 Γ— 10⁹⁸(99-digit number)
30259471529112151983…21945814600059453439
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 3506691

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 8506fdd7896b6cb2e8d47a4ee1c8e13a31b297950eb906c796b3c06bbfc08e5d

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 #3,506,691 on Chainz β†—
Circulating Supply:58,001,896 XPMΒ·at block #6,844,685 Β· updates every 60s
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