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Home/Chain Registry/Block #1,481,105

Block #1,481,105

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/3/2016, 2:07:31 AM Β· Difficulty 10.7203 Β· 5,363,859 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4e43d74cc7e01b4bd0b2f1daf11036c1864397b9a2e34728b42c3bb4935b9a29
View on Chainz β†—

Difficulty

10.720335

Transactions

1

Size

200 B

Version

2

Bits

0ab867d8

Nonce

756,348,540

Timestamp

3/3/2016, 2:07:31 AM

Confirmations

5,363,859

Merkle Root

4c37d8a714beb22af3c9920932274c3356549e41a174657e11577d76e8ba7b8b
Transactions (1)
Coinbase4c37d8a714beb2…577d76e8ba7b8b
1 in β†’ 1 out8.6900 XPM110 B
AQe5imnZ…6ozJ2X5S
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.

9.245 Γ— 10⁹³(94-digit number)
92451994246047946569…84490444551618589120
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
9.245 Γ— 10⁹³(94-digit number)
92451994246047946569…84490444551618589121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.849 Γ— 10⁹⁴(95-digit number)
18490398849209589313…68980889103237178241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.698 Γ— 10⁹⁴(95-digit number)
36980797698419178627…37961778206474356481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.396 Γ— 10⁹⁴(95-digit number)
73961595396838357255…75923556412948712961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.479 Γ— 10⁹⁡(96-digit number)
14792319079367671451…51847112825897425921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.958 Γ— 10⁹⁡(96-digit number)
29584638158735342902…03694225651794851841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.916 Γ— 10⁹⁡(96-digit number)
59169276317470685804…07388451303589703681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.183 Γ— 10⁹⁢(97-digit number)
11833855263494137160…14776902607179407361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.366 Γ— 10⁹⁢(97-digit number)
23667710526988274321…29553805214358814721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.733 Γ— 10⁹⁢(97-digit number)
47335421053976548643…59107610428717629441
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 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
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 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 1481105

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 4e43d74cc7e01b4bd0b2f1daf11036c1864397b9a2e34728b42c3bb4935b9a29

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 #1,481,105 on Chainz β†—
Circulating Supply:58,004,131 XPMΒ·at block #6,844,963 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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