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Home/Chain Registry/Block #2,653,574

Block #2,653,574

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/8/2018, 12:33:35 PM Β· Difficulty 11.7358 Β· 4,178,019 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1309b458fdcec9dbc37bd4a82472521236b859820485101a816cc340fd01be0b
View on Chainz β†—

Difficulty

11.735832

Transactions

1

Size

201 B

Version

2

Bits

0bbc5f7a

Nonce

717,574,475

Timestamp

5/8/2018, 12:33:35 PM

Confirmations

4,178,019

Merkle Root

6bed6e89e268c558b9ba2ceb668d44c48930087817bc9586e1c788df4c282a27
Transactions (1)
Coinbase6bed6e89e268c5…c788df4c282a27
1 in β†’ 1 out7.2500 XPM110 B
Abjd2Et7…gnfdbsEk
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.

5.317 Γ— 10⁹⁢(97-digit number)
53178135521376107906…44298345576112230400
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
5.317 Γ— 10⁹⁢(97-digit number)
53178135521376107906…44298345576112230399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.063 Γ— 10⁹⁷(98-digit number)
10635627104275221581…88596691152224460799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.127 Γ— 10⁹⁷(98-digit number)
21271254208550443162…77193382304448921599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.254 Γ— 10⁹⁷(98-digit number)
42542508417100886325…54386764608897843199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.508 Γ— 10⁹⁷(98-digit number)
85085016834201772650…08773529217795686399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.701 Γ— 10⁹⁸(99-digit number)
17017003366840354530…17547058435591372799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.403 Γ— 10⁹⁸(99-digit number)
34034006733680709060…35094116871182745599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.806 Γ— 10⁹⁸(99-digit number)
68068013467361418120…70188233742365491199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.361 Γ— 10⁹⁹(100-digit number)
13613602693472283624…40376467484730982399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.722 Γ— 10⁹⁹(100-digit number)
27227205386944567248…80752934969461964799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.445 Γ— 10⁹⁹(100-digit number)
54454410773889134496…61505869938923929599
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 2653574

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 1309b458fdcec9dbc37bd4a82472521236b859820485101a816cc340fd01be0b

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 #2,653,574 on Chainz β†—
Circulating Supply:57,896,840 XPMΒ·at block #6,831,592 Β· updates every 60s
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