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Home/Chain Registry/Block #3,451,210

Block #3,451,210

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/27/2019, 12:04:58 PM Β· Difficulty 10.9794 Β· 3,391,192 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
68fd379964adea7e3dfd0a55536065666e36706a633d503509813df4c7a47d51
View on Chainz β†—

Difficulty

10.979376

Transactions

1

Size

200 B

Version

2

Bits

0afab868

Nonce

790,992,316

Timestamp

11/27/2019, 12:04:58 PM

Confirmations

3,391,192

Merkle Root

9ad8a14521bbbde22f05416f15ef4c29630df7a1c4e5ea6cc86b81c8f01abf5c
Transactions (1)
Coinbase9ad8a14521bbbd…6b81c8f01abf5c
1 in β†’ 1 out8.2800 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.

7.754 Γ— 10⁹⁡(96-digit number)
77542640888618719110…42779996614510510080
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
7.754 Γ— 10⁹⁡(96-digit number)
77542640888618719110…42779996614510510079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.550 Γ— 10⁹⁢(97-digit number)
15508528177723743822…85559993229021020159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.101 Γ— 10⁹⁢(97-digit number)
31017056355447487644…71119986458042040319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.203 Γ— 10⁹⁢(97-digit number)
62034112710894975288…42239972916084080639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.240 Γ— 10⁹⁷(98-digit number)
12406822542178995057…84479945832168161279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.481 Γ— 10⁹⁷(98-digit number)
24813645084357990115…68959891664336322559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.962 Γ— 10⁹⁷(98-digit number)
49627290168715980230…37919783328672645119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.925 Γ— 10⁹⁷(98-digit number)
99254580337431960461…75839566657345290239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.985 Γ— 10⁹⁸(99-digit number)
19850916067486392092…51679133314690580479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.970 Γ— 10⁹⁸(99-digit number)
39701832134972784184…03358266629381160959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.940 Γ— 10⁹⁸(99-digit number)
79403664269945568368…06716533258762321919
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 3451210

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 68fd379964adea7e3dfd0a55536065666e36706a633d503509813df4c7a47d51

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 #3,451,210 on Chainz β†—
Circulating Supply:57,983,627 XPMΒ·at block #6,842,401 Β· updates every 60s
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