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Home/Chain Registry/Block #292,821

Block #292,821

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/3/2013, 11:16:35 PM Β· Difficulty 9.9904 Β· 6,534,517 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
52f5e827dfaba362ee86c93e96a74e13296f632743524b82c78f0be6f9b970e1
View on Chainz β†—

Height

#292,821

Difficulty

9.990418

Transactions

1

Size

208 B

Version

2

Bits

09fd8c0d

Nonce

5,793

Timestamp

12/3/2013, 11:16:35 PM

Confirmations

6,534,517

Merkle Root

9515672f2f8fee7f86efd46350e9714ce15dcd8ee8f2daff9c3c7c381b877d4e
Transactions (1)
Coinbase9515672f2f8fee…3c7c381b877d4e
1 in β†’ 1 out10.0000 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.871 Γ— 10¹⁰⁰(101-digit number)
28719312890610603084…99337064434830131200
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
2.871 Γ— 10¹⁰⁰(101-digit number)
28719312890610603084…99337064434830131201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.743 Γ— 10¹⁰⁰(101-digit number)
57438625781221206168…98674128869660262401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.148 Γ— 10¹⁰¹(102-digit number)
11487725156244241233…97348257739320524801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.297 Γ— 10¹⁰¹(102-digit number)
22975450312488482467…94696515478641049601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.595 Γ— 10¹⁰¹(102-digit number)
45950900624976964935…89393030957282099201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.190 Γ— 10¹⁰¹(102-digit number)
91901801249953929870…78786061914564198401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.838 Γ— 10¹⁰²(103-digit number)
18380360249990785974…57572123829128396801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.676 Γ— 10¹⁰²(103-digit number)
36760720499981571948…15144247658256793601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.352 Γ— 10¹⁰²(103-digit number)
73521440999963143896…30288495316513587201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.470 Γ— 10¹⁰³(104-digit number)
14704288199992628779…60576990633027174401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.940 Γ— 10¹⁰³(104-digit number)
29408576399985257558…21153981266054348801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
5.881 Γ— 10¹⁰³(104-digit number)
58817152799970515116…42307962532108697601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 292821

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 52f5e827dfaba362ee86c93e96a74e13296f632743524b82c78f0be6f9b970e1

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 #292,821 on Chainz β†—
Circulating Supply:57,862,812 XPMΒ·at block #6,827,337 Β· updates every 60s
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