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Block #580,515

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/7/2014, 8:44:58 PM Β· Difficulty 10.9649 Β· 6,215,004 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ab07c7c2d2033b94ff476cc27f654b8e95ae1f45741edd4be6c5f25d55c52693
View on Chainz β†—

Height

#580,515

Difficulty

10.964880

Transactions

1

Size

208 B

Version

2

Bits

0af7025e

Nonce

698,005,470

Timestamp

6/7/2014, 8:44:58 PM

Confirmations

6,215,004

Merkle Root

a1dda49cdb3e9c9b511e30a2f913a62c6054c425045b9ae24c4a41eab72f3ad6
Transactions (1)
Coinbasea1dda49cdb3e9c…4a41eab72f3ad6
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.

2.203 Γ— 10⁹⁹(100-digit number)
22030253114439530549…38287640547262725120
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
2.203 Γ— 10⁹⁹(100-digit number)
22030253114439530549…38287640547262725121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.406 Γ— 10⁹⁹(100-digit number)
44060506228879061098…76575281094525450241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.812 Γ— 10⁹⁹(100-digit number)
88121012457758122197…53150562189050900481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.762 Γ— 10¹⁰⁰(101-digit number)
17624202491551624439…06301124378101800961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.524 Γ— 10¹⁰⁰(101-digit number)
35248404983103248879…12602248756203601921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.049 Γ— 10¹⁰⁰(101-digit number)
70496809966206497758…25204497512407203841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.409 Γ— 10¹⁰¹(102-digit number)
14099361993241299551…50408995024814407681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.819 Γ— 10¹⁰¹(102-digit number)
28198723986482599103…00817990049628815361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.639 Γ— 10¹⁰¹(102-digit number)
56397447972965198206…01635980099257630721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.127 Γ— 10¹⁰²(103-digit number)
11279489594593039641…03271960198515261441
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 580515

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 ab07c7c2d2033b94ff476cc27f654b8e95ae1f45741edd4be6c5f25d55c52693

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 #580,515 on Chainz β†—
Circulating Supply:57,608,213 XPMΒ·at block #6,795,518 Β· updates every 60s
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