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Block #2,473,056

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/14/2018, 6:23:27 PM Β· Difficulty 10.9632 Β· 4,372,561 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
51989318f7deafab9825f22def553a5ef38cfada82f81090039a82799d584d4d
View on Chainz β†—

Difficulty

10.963179

Transactions

1

Size

200 B

Version

2

Bits

0af692e7

Nonce

1,377,942,633

Timestamp

1/14/2018, 6:23:27 PM

Confirmations

4,372,561

Merkle Root

dff3a9a031d3970a4c395b8862ce06074915878fa720794e601ec67c40fa0d57
Transactions (1)
Coinbasedff3a9a031d397…1ec67c40fa0d57
1 in β†’ 1 out8.3100 XPM110 B
AG2JSUCM…5nnGEHea
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.

1.783 Γ— 10⁹⁡(96-digit number)
17837907340259172018…77087226174374153600
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
1.783 Γ— 10⁹⁡(96-digit number)
17837907340259172018…77087226174374153599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.567 Γ— 10⁹⁡(96-digit number)
35675814680518344037…54174452348748307199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.135 Γ— 10⁹⁡(96-digit number)
71351629361036688075…08348904697496614399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.427 Γ— 10⁹⁢(97-digit number)
14270325872207337615…16697809394993228799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.854 Γ— 10⁹⁢(97-digit number)
28540651744414675230…33395618789986457599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.708 Γ— 10⁹⁢(97-digit number)
57081303488829350460…66791237579972915199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.141 Γ— 10⁹⁷(98-digit number)
11416260697765870092…33582475159945830399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.283 Γ— 10⁹⁷(98-digit number)
22832521395531740184…67164950319891660799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.566 Γ— 10⁹⁷(98-digit number)
45665042791063480368…34329900639783321599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.133 Γ— 10⁹⁷(98-digit number)
91330085582126960736…68659801279566643199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.826 Γ— 10⁹⁸(99-digit number)
18266017116425392147…37319602559133286399
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 2473056

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 51989318f7deafab9825f22def553a5ef38cfada82f81090039a82799d584d4d

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 #2,473,056 on Chainz β†—
Circulating Supply:58,009,383 XPMΒ·at block #6,845,616 Β· updates every 60s
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