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Home/Chain Registry/Block #3,055,893

Block #3,055,893

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/16/2019, 9:02:59 PM Β· Difficulty 11.0085 Β· 3,770,499 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2b9691a5862bfa0ba1fca526675ee00d18f50203255453c7b46e224ebec6f368
View on Chainz β†—

Difficulty

11.008480

Transactions

1

Size

201 B

Version

2

Bits

0b022bba

Nonce

1,034,202,104

Timestamp

2/16/2019, 9:02:59 PM

Confirmations

3,770,499

Merkle Root

7a761be7b290dbf90eeefe7931f382d1e3bfa871cbf7134d5627d04a513522e8
Transactions (1)
Coinbase7a761be7b290db…27d04a513522e8
1 in β†’ 1 out8.2400 XPM110 B
AbXwmGxD…4XXYP765
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.

1.622 Γ— 10⁹⁢(97-digit number)
16228083269973219702…95733604469617203200
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.622 Γ— 10⁹⁢(97-digit number)
16228083269973219702…95733604469617203201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.245 Γ— 10⁹⁢(97-digit number)
32456166539946439405…91467208939234406401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.491 Γ— 10⁹⁢(97-digit number)
64912333079892878810…82934417878468812801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.298 Γ— 10⁹⁷(98-digit number)
12982466615978575762…65868835756937625601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.596 Γ— 10⁹⁷(98-digit number)
25964933231957151524…31737671513875251201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.192 Γ— 10⁹⁷(98-digit number)
51929866463914303048…63475343027750502401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.038 Γ— 10⁹⁸(99-digit number)
10385973292782860609…26950686055501004801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.077 Γ— 10⁹⁸(99-digit number)
20771946585565721219…53901372111002009601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.154 Γ— 10⁹⁸(99-digit number)
41543893171131442438…07802744222004019201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.308 Γ— 10⁹⁸(99-digit number)
83087786342262884877…15605488444008038401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.661 Γ— 10⁹⁹(100-digit number)
16617557268452576975…31210976888016076801
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 3055893

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 2b9691a5862bfa0ba1fca526675ee00d18f50203255453c7b46e224ebec6f368

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 #3,055,893 on Chainz β†—
Circulating Supply:57,855,275 XPMΒ·at block #6,826,391 Β· updates every 60s
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