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Home/Chain Registry/Block #1,597,205

Block #1,597,205

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/23/2016, 10:03:47 PM Β· Difficulty 10.6112 Β· 5,245,616 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0c0f8c7c6ab8eced6535da27bf9b23107214f39b48a4c73922da9864d5cf3948
View on Chainz β†—

Difficulty

10.611229

Transactions

1

Size

242 B

Version

2

Bits

0a9c797a

Nonce

422,151,934

Timestamp

5/23/2016, 10:03:47 PM

Confirmations

5,245,616

Merkle Root

d0181028a4bb2eb87019fe910a0bf4935912ce52838b3d632c9e871d1fc1d3f1
Transactions (1)
Coinbased0181028a4bb2e…9e871d1fc1d3f1
1 in β†’ 2 out8.8700 XPM152 B
AXZf8xqq…hQwCQgXtALPu3s2c…EJXLjVFh
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.

2.320 Γ— 10⁹⁴(95-digit number)
23207737326287461171…97574790239676624640
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
2.320 Γ— 10⁹⁴(95-digit number)
23207737326287461171…97574790239676624641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.641 Γ— 10⁹⁴(95-digit number)
46415474652574922343…95149580479353249281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.283 Γ— 10⁹⁴(95-digit number)
92830949305149844686…90299160958706498561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.856 Γ— 10⁹⁡(96-digit number)
18566189861029968937…80598321917412997121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.713 Γ— 10⁹⁡(96-digit number)
37132379722059937874…61196643834825994241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.426 Γ— 10⁹⁡(96-digit number)
74264759444119875748…22393287669651988481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.485 Γ— 10⁹⁢(97-digit number)
14852951888823975149…44786575339303976961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.970 Γ— 10⁹⁢(97-digit number)
29705903777647950299…89573150678607953921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.941 Γ— 10⁹⁢(97-digit number)
59411807555295900599…79146301357215907841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.188 Γ— 10⁹⁷(98-digit number)
11882361511059180119…58292602714431815681
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 1597205

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 0c0f8c7c6ab8eced6535da27bf9b23107214f39b48a4c73922da9864d5cf3948

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 #1,597,205 on Chainz β†—
Circulating Supply:57,986,909 XPMΒ·at block #6,842,820 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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