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Home/Chain Registry/Block #1,598,452

Block #1,598,452

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/24/2016, 7:07:15 PM Β· Difficulty 10.6099 Β· 5,247,198 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
87668f847b7b11722ffdc250f7a91a5596967c71254a3a6e5f6c86cdf16746ed
View on Chainz β†—

Difficulty

10.609937

Transactions

1

Size

199 B

Version

2

Bits

0a9c24d7

Nonce

22,690,813

Timestamp

5/24/2016, 7:07:15 PM

Confirmations

5,247,198

Merkle Root

a24f772ba630260370e9ceb3888f4897830fb5398c9c970d40326156411f78e2
Transactions (1)
Coinbasea24f772ba63026…326156411f78e2
1 in β†’ 1 out8.8700 XPM109 B
AKKxraiC…Rmqxw9rY
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.

1.936 Γ— 10⁹⁡(96-digit number)
19364251874230345566…66575017163764817920
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
1.936 Γ— 10⁹⁡(96-digit number)
19364251874230345566…66575017163764817921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.872 Γ— 10⁹⁡(96-digit number)
38728503748460691133…33150034327529635841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.745 Γ— 10⁹⁡(96-digit number)
77457007496921382266…66300068655059271681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.549 Γ— 10⁹⁢(97-digit number)
15491401499384276453…32600137310118543361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.098 Γ— 10⁹⁢(97-digit number)
30982802998768552906…65200274620237086721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.196 Γ— 10⁹⁢(97-digit number)
61965605997537105813…30400549240474173441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.239 Γ— 10⁹⁷(98-digit number)
12393121199507421162…60801098480948346881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.478 Γ— 10⁹⁷(98-digit number)
24786242399014842325…21602196961896693761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.957 Γ— 10⁹⁷(98-digit number)
49572484798029684650…43204393923793387521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.914 Γ— 10⁹⁷(98-digit number)
99144969596059369301…86408787847586775041
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 1598452

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 87668f847b7b11722ffdc250f7a91a5596967c71254a3a6e5f6c86cdf16746ed

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 #1,598,452 on Chainz β†—
Circulating Supply:58,009,649 XPMΒ·at block #6,845,649 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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