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Home/Chain Registry/Block #1,365,137

Block #1,365,137

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/11/2015, 9:39:02 AM Β· Difficulty 10.8459 Β· 5,461,850 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ae418c4c68ccad7fc3d5a728b6fa1df49d3c983242a25237bb786ddf6836693b
View on Chainz β†—

Difficulty

10.845905

Transactions

1

Size

198 B

Version

2

Bits

0ad88d43

Nonce

572,904,031

Timestamp

12/11/2015, 9:39:02 AM

Confirmations

5,461,850

Merkle Root

8531e7137f97d9a4b005126f99a1680cbee9df5ec79a65a670a59aecb0b0e203
Transactions (1)
Coinbase8531e7137f97d9…a59aecb0b0e203
1 in β†’ 1 out8.4900 XPM109 B
ALKZakxV…WmnmEhua
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.

2.781 Γ— 10⁹²(93-digit number)
27819539435314250815…44401986280970929920
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
2.781 Γ— 10⁹²(93-digit number)
27819539435314250815…44401986280970929919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.563 Γ— 10⁹²(93-digit number)
55639078870628501630…88803972561941859839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.112 Γ— 10⁹³(94-digit number)
11127815774125700326…77607945123883719679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.225 Γ— 10⁹³(94-digit number)
22255631548251400652…55215890247767439359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.451 Γ— 10⁹³(94-digit number)
44511263096502801304…10431780495534878719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.902 Γ— 10⁹³(94-digit number)
89022526193005602608…20863560991069757439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.780 Γ— 10⁹⁴(95-digit number)
17804505238601120521…41727121982139514879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.560 Γ— 10⁹⁴(95-digit number)
35609010477202241043…83454243964279029759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.121 Γ— 10⁹⁴(95-digit number)
71218020954404482086…66908487928558059519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.424 Γ— 10⁹⁡(96-digit number)
14243604190880896417…33816975857116119039
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 1365137

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 ae418c4c68ccad7fc3d5a728b6fa1df49d3c983242a25237bb786ddf6836693b

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 #1,365,137 on Chainz β†—
Circulating Supply:57,860,071 XPMΒ·at block #6,826,986 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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