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Home/Chain Registry/Block #1,411,045

Block #1,411,045

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/13/2016, 3:06:55 AM Β· Difficulty 10.8054 Β· 5,433,461 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
caf1855d55be960887512495be75f42f21350d7eec9357d06ae23faae8950858
View on Chainz β†—

Difficulty

10.805378

Transactions

1

Size

200 B

Version

2

Bits

0ace2d3c

Nonce

124,246,140

Timestamp

1/13/2016, 3:06:55 AM

Confirmations

5,433,461

Merkle Root

63cd81d3b7cfeacc0a66320e90e8f4203b1e39cc4c725e2f546a82ff0862f33a
Transactions (1)
Coinbase63cd81d3b7cfea…6a82ff0862f33a
1 in β†’ 1 out8.5500 XPM110 B
AUkrm2Ph…5Py6sEsZ
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.

2.877 Γ— 10⁹⁴(95-digit number)
28777893217195160120…79650966958162819840
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
2.877 Γ— 10⁹⁴(95-digit number)
28777893217195160120…79650966958162819839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.755 Γ— 10⁹⁴(95-digit number)
57555786434390320240…59301933916325639679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.151 Γ— 10⁹⁡(96-digit number)
11511157286878064048…18603867832651279359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.302 Γ— 10⁹⁡(96-digit number)
23022314573756128096…37207735665302558719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.604 Γ— 10⁹⁡(96-digit number)
46044629147512256192…74415471330605117439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.208 Γ— 10⁹⁡(96-digit number)
92089258295024512385…48830942661210234879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.841 Γ— 10⁹⁢(97-digit number)
18417851659004902477…97661885322420469759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.683 Γ— 10⁹⁢(97-digit number)
36835703318009804954…95323770644840939519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.367 Γ— 10⁹⁢(97-digit number)
73671406636019609908…90647541289681879039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.473 Γ— 10⁹⁷(98-digit number)
14734281327203921981…81295082579363758079
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 1411045

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 caf1855d55be960887512495be75f42f21350d7eec9357d06ae23faae8950858

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 #1,411,045 on Chainz β†—
Circulating Supply:58,000,446 XPMΒ·at block #6,844,505 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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