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Block #559,620

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/24/2014, 7:40:41 AM Β· Difficulty 10.9645 Β· 6,264,876 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
25bed27eb23e13e15280660dea3da3be95da417109f31bf2293e143ff0b6f157
View on Chainz β†—

Height

#559,620

Difficulty

10.964540

Transactions

1

Size

208 B

Version

2

Bits

0af6ec1e

Nonce

143,147,473

Timestamp

5/24/2014, 7:40:41 AM

Confirmations

6,264,876

Merkle Root

eecbc3aaf4ff769708c0fabcffc8f51a98049cfbf58b5b365df02b985f19b308
Transactions (1)
Coinbaseeecbc3aaf4ff76…f02b985f19b308
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

4.092 Γ— 10⁹⁹(100-digit number)
40929853971980539334…40505295156149664640
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
4.092 Γ— 10⁹⁹(100-digit number)
40929853971980539334…40505295156149664641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.185 Γ— 10⁹⁹(100-digit number)
81859707943961078668…81010590312299329281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.637 Γ— 10¹⁰⁰(101-digit number)
16371941588792215733…62021180624598658561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.274 Γ— 10¹⁰⁰(101-digit number)
32743883177584431467…24042361249197317121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.548 Γ— 10¹⁰⁰(101-digit number)
65487766355168862934…48084722498394634241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.309 Γ— 10¹⁰¹(102-digit number)
13097553271033772586…96169444996789268481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.619 Γ— 10¹⁰¹(102-digit number)
26195106542067545173…92338889993578536961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.239 Γ— 10¹⁰¹(102-digit number)
52390213084135090347…84677779987157073921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.047 Γ— 10¹⁰²(103-digit number)
10478042616827018069…69355559974314147841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.095 Γ— 10¹⁰²(103-digit number)
20956085233654036139…38711119948628295681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.191 Γ— 10¹⁰²(103-digit number)
41912170467308072278…77422239897256591361
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 559620

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 25bed27eb23e13e15280660dea3da3be95da417109f31bf2293e143ff0b6f157

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 #559,620 on Chainz β†—
Circulating Supply:57,840,040 XPMΒ·at block #6,824,495 Β· updates every 60s
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