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Home/Chain Registry/Block #1,112,457

Block #1,112,457

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/17/2015, 7:37:58 AM Β· Difficulty 10.8958 Β· 5,704,141 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7dfd591044827f0a0c3d9a96d8157dcd59f731ee1c6dfaa57abe0fd86bba2afe
View on Chainz β†—

Difficulty

10.895772

Transactions

1

Size

201 B

Version

2

Bits

0ae5514a

Nonce

1,034,778,784

Timestamp

6/17/2015, 7:37:58 AM

Confirmations

5,704,141

Merkle Root

75e94a95b43bf510cf6984d368f27e1f2b3882130622884e9c96b91326e04ce8
Transactions (1)
Coinbase75e94a95b43bf5…96b91326e04ce8
1 in β†’ 1 out8.4100 XPM110 B
AThe7C9J…qBvMHMPt
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.

6.551 Γ— 10⁹⁷(98-digit number)
65512029869835916135…86119997288712366080
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
6.551 Γ— 10⁹⁷(98-digit number)
65512029869835916135…86119997288712366079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.310 Γ— 10⁹⁸(99-digit number)
13102405973967183227…72239994577424732159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.620 Γ— 10⁹⁸(99-digit number)
26204811947934366454…44479989154849464319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.240 Γ— 10⁹⁸(99-digit number)
52409623895868732908…88959978309698928639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.048 Γ— 10⁹⁹(100-digit number)
10481924779173746581…77919956619397857279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.096 Γ— 10⁹⁹(100-digit number)
20963849558347493163…55839913238795714559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.192 Γ— 10⁹⁹(100-digit number)
41927699116694986326…11679826477591429119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.385 Γ— 10⁹⁹(100-digit number)
83855398233389972653…23359652955182858239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.677 Γ— 10¹⁰⁰(101-digit number)
16771079646677994530…46719305910365716479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.354 Γ— 10¹⁰⁰(101-digit number)
33542159293355989061…93438611820731432959
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1112457

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 7dfd591044827f0a0c3d9a96d8157dcd59f731ee1c6dfaa57abe0fd86bba2afe

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 #1,112,457 on Chainz β†—
Circulating Supply:57,776,909 XPMΒ·at block #6,816,597 Β· updates every 60s
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