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Block #586,773

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/13/2014, 7:06:18 AM Β· Difficulty 10.9524 Β· 6,240,147 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4b7a0994caafcf896c6f7f9af3d4bb87d7b42143fd8123d5b49f6863115a08c4
View on Chainz β†—

Height

#586,773

Difficulty

10.952370

Transactions

1

Size

203 B

Version

2

Bits

0af3ce8a

Nonce

48,607

Timestamp

6/13/2014, 7:06:18 AM

Confirmations

6,240,147

Merkle Root

f951b490eb786ca559b083330e1556570464ce97045d32adbe3fd674e0a2f4a7
Transactions (1)
Coinbasef951b490eb786c…3fd674e0a2f4a7
1 in β†’ 1 out8.3200 XPM110 B
AeKNrjNj…1NEq95Ta
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.

3.812 Γ— 10¹⁰¹(102-digit number)
38127250833081412281…23023201964930021440
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
3.812 Γ— 10¹⁰¹(102-digit number)
38127250833081412281…23023201964930021441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.625 Γ— 10¹⁰¹(102-digit number)
76254501666162824563…46046403929860042881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.525 Γ— 10¹⁰²(103-digit number)
15250900333232564912…92092807859720085761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.050 Γ— 10¹⁰²(103-digit number)
30501800666465129825…84185615719440171521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.100 Γ— 10¹⁰²(103-digit number)
61003601332930259651…68371231438880343041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.220 Γ— 10¹⁰³(104-digit number)
12200720266586051930…36742462877760686081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.440 Γ— 10¹⁰³(104-digit number)
24401440533172103860…73484925755521372161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.880 Γ— 10¹⁰³(104-digit number)
48802881066344207720…46969851511042744321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.760 Γ— 10¹⁰³(104-digit number)
97605762132688415441…93939703022085488641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.952 Γ— 10¹⁰⁴(105-digit number)
19521152426537683088…87879406044170977281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.904 Γ— 10¹⁰⁴(105-digit number)
39042304853075366176…75758812088341954561
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 586773

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 4b7a0994caafcf896c6f7f9af3d4bb87d7b42143fd8123d5b49f6863115a08c4

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 #586,773 on Chainz β†—
Circulating Supply:57,859,530 XPMΒ·at block #6,826,919 Β· updates every 60s
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