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Home/Chain Registry/Block #1,113,480

Block #1,113,480

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/17/2015, 4:42:49 PM Β· Difficulty 10.9052 Β· 5,725,392 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
282b78ee6a40aa5937f0903c21f993800fca3be6081e6313dc643db2d63b8794
View on Chainz β†—

Difficulty

10.905227

Transactions

1

Size

207 B

Version

2

Bits

0ae7bcef

Nonce

2,829,897,258

Timestamp

6/17/2015, 4:42:49 PM

Confirmations

5,725,392

Merkle Root

e280579c2beb3a36c03189467bce3bfe3988fe37aca53703842834930ef169e5
Transactions (1)
Coinbasee280579c2beb3a…2834930ef169e5
1 in β†’ 1 out8.4000 XPM116 B
AJCEY9yy…tg97E6zm
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.

1.014 Γ— 10⁹⁢(97-digit number)
10143995940422278756…36869064795828161920
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
1.014 Γ— 10⁹⁢(97-digit number)
10143995940422278756…36869064795828161921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.028 Γ— 10⁹⁢(97-digit number)
20287991880844557513…73738129591656323841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.057 Γ— 10⁹⁢(97-digit number)
40575983761689115026…47476259183312647681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.115 Γ— 10⁹⁢(97-digit number)
81151967523378230053…94952518366625295361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.623 Γ— 10⁹⁷(98-digit number)
16230393504675646010…89905036733250590721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.246 Γ— 10⁹⁷(98-digit number)
32460787009351292021…79810073466501181441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.492 Γ— 10⁹⁷(98-digit number)
64921574018702584042…59620146933002362881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.298 Γ— 10⁹⁸(99-digit number)
12984314803740516808…19240293866004725761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.596 Γ— 10⁹⁸(99-digit number)
25968629607481033617…38480587732009451521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.193 Γ— 10⁹⁸(99-digit number)
51937259214962067234…76961175464018903041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.038 Γ— 10⁹⁹(100-digit number)
10387451842992413446…53922350928037806081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
2.077 Γ— 10⁹⁹(100-digit number)
20774903685984826893…07844701856075612161
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 1113480

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 282b78ee6a40aa5937f0903c21f993800fca3be6081e6313dc643db2d63b8794

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 #1,113,480 on Chainz β†—
Circulating Supply:57,955,242 XPMΒ·at block #6,838,871 Β· updates every 60s
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