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Home/Chain Registry/Block #3,003,623

Block #3,003,623

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/10/2019, 1:35:37 PM Β· Difficulty 11.2089 Β· 3,832,971 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2c5fbfc88465a26aa12d625949627b2440825c4d78353dbfbfd8e04437d08b6f
View on Chainz β†—

Difficulty

11.208888

Transactions

1

Size

201 B

Version

2

Bits

0b3579af

Nonce

591,881,155

Timestamp

1/10/2019, 1:35:37 PM

Confirmations

3,832,971

Merkle Root

c4442d486bc8dd0de4f5760705dc6f9d76b327ef47a488de016fc8fe5a9f3df3
Transactions (1)
Coinbasec4442d486bc8dd…6fc8fe5a9f3df3
1 in β†’ 1 out7.9500 XPM110 B
AUMQRepm…tAfKmdW1
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.

7.644 Γ— 10⁹⁡(96-digit number)
76443583990602783316…33062126641994475520
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
7.644 Γ— 10⁹⁡(96-digit number)
76443583990602783316…33062126641994475521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.528 Γ— 10⁹⁢(97-digit number)
15288716798120556663…66124253283988951041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.057 Γ— 10⁹⁢(97-digit number)
30577433596241113326…32248506567977902081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.115 Γ— 10⁹⁢(97-digit number)
61154867192482226652…64497013135955804161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.223 Γ— 10⁹⁷(98-digit number)
12230973438496445330…28994026271911608321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.446 Γ— 10⁹⁷(98-digit number)
24461946876992890661…57988052543823216641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.892 Γ— 10⁹⁷(98-digit number)
48923893753985781322…15976105087646433281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.784 Γ— 10⁹⁷(98-digit number)
97847787507971562644…31952210175292866561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.956 Γ— 10⁹⁸(99-digit number)
19569557501594312528…63904420350585733121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.913 Γ— 10⁹⁸(99-digit number)
39139115003188625057…27808840701171466241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.827 Γ— 10⁹⁸(99-digit number)
78278230006377250115…55617681402342932481
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 3003623

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 2c5fbfc88465a26aa12d625949627b2440825c4d78353dbfbfd8e04437d08b6f

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 #3,003,623 on Chainz β†—
Circulating Supply:57,937,022 XPMΒ·at block #6,836,593 Β· updates every 60s
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