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Home/Chain Registry/Block #3,546,824

Block #3,546,824

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/6/2020, 6:10:56 AM Β· Difficulty 10.9340 Β· 3,286,952 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
90dbbdd2943a5102ba7b14d51f8e4fac0e8f837ce93b1bb647b2f610c4c7a6e7
View on Chainz β†—

Difficulty

10.934028

Transactions

1

Size

201 B

Version

2

Bits

0aef1c6e

Nonce

451,293,331

Timestamp

2/6/2020, 6:10:56 AM

Confirmations

3,286,952

Merkle Root

926dd842831005e7116352dfd24dec0ca6ab176cb9074c5dea7be548957b0a1f
Transactions (1)
Coinbase926dd842831005…7be548957b0a1f
1 in β†’ 1 out8.3500 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.

7.790 Γ— 10⁹⁢(97-digit number)
77901413663850331946…36535637889687139840
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
7.790 Γ— 10⁹⁢(97-digit number)
77901413663850331946…36535637889687139839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.558 Γ— 10⁹⁷(98-digit number)
15580282732770066389…73071275779374279679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.116 Γ— 10⁹⁷(98-digit number)
31160565465540132778…46142551558748559359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.232 Γ— 10⁹⁷(98-digit number)
62321130931080265557…92285103117497118719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.246 Γ— 10⁹⁸(99-digit number)
12464226186216053111…84570206234994237439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.492 Γ— 10⁹⁸(99-digit number)
24928452372432106222…69140412469988474879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.985 Γ— 10⁹⁸(99-digit number)
49856904744864212445…38280824939976949759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.971 Γ— 10⁹⁸(99-digit number)
99713809489728424891…76561649879953899519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.994 Γ— 10⁹⁹(100-digit number)
19942761897945684978…53123299759907799039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.988 Γ— 10⁹⁹(100-digit number)
39885523795891369956…06246599519815598079
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 3546824

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 90dbbdd2943a5102ba7b14d51f8e4fac0e8f837ce93b1bb647b2f610c4c7a6e7

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 #3,546,824 on Chainz β†—
Circulating Supply:57,914,426 XPMΒ·at block #6,833,775 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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