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Home/Chain Registry/Block #2,473,057

Block #2,473,057

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/14/2018, 6:24:13 PM Β· Difficulty 10.9632 Β· 4,369,205 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2f1d6895f0dbbf97a8492b3b522c252cd2c0d70e8ade2789dbdfe44f4f90d35b
View on Chainz β†—

Difficulty

10.963180

Transactions

1

Size

201 B

Version

2

Bits

0af692f4

Nonce

1,926,883,356

Timestamp

1/14/2018, 6:24:13 PM

Confirmations

4,369,205

Merkle Root

75de0ee3bca8c1a66b2b37869a8397e40cc65b77990e47032b3b80e482d0126d
Transactions (1)
Coinbase75de0ee3bca8c1…3b80e482d0126d
1 in β†’ 1 out8.3100 XPM110 B
AdXEDotW…9XsBqQzR
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.

1.794 Γ— 10⁹⁢(97-digit number)
17946270120880727238…85966342801038489600
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
1.794 Γ— 10⁹⁢(97-digit number)
17946270120880727238…85966342801038489601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.589 Γ— 10⁹⁢(97-digit number)
35892540241761454477…71932685602076979201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.178 Γ— 10⁹⁢(97-digit number)
71785080483522908955…43865371204153958401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.435 Γ— 10⁹⁷(98-digit number)
14357016096704581791…87730742408307916801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.871 Γ— 10⁹⁷(98-digit number)
28714032193409163582…75461484816615833601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.742 Γ— 10⁹⁷(98-digit number)
57428064386818327164…50922969633231667201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.148 Γ— 10⁹⁸(99-digit number)
11485612877363665432…01845939266463334401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.297 Γ— 10⁹⁸(99-digit number)
22971225754727330865…03691878532926668801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.594 Γ— 10⁹⁸(99-digit number)
45942451509454661731…07383757065853337601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.188 Γ— 10⁹⁸(99-digit number)
91884903018909323462…14767514131706675201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.837 Γ— 10⁹⁹(100-digit number)
18376980603781864692…29535028263413350401
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 2473057

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 2f1d6895f0dbbf97a8492b3b522c252cd2c0d70e8ade2789dbdfe44f4f90d35b

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 #2,473,057 on Chainz β†—
Circulating Supply:57,982,494 XPMΒ·at block #6,842,261 Β· updates every 60s
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