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Block #279,092

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/28/2013, 5:45:28 AM Β· Difficulty 9.9707 Β· 6,536,847 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4d6216f5297dfebdeb45e08126a208c22e2bb58b5efa461d4e0e2755971c16d6
View on Chainz β†—

Height

#279,092

Difficulty

9.970726

Transactions

1

Size

207 B

Version

2

Bits

09f8817b

Nonce

193,524

Timestamp

11/28/2013, 5:45:28 AM

Confirmations

6,536,847

Merkle Root

896c6ec402d18c139c81747f6f0381ba299de3739b8db3d45f87ff959993de9b
Transactions (1)
Coinbase896c6ec402d18c…87ff959993de9b
1 in β†’ 1 out10.0400 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.

1.961 Γ— 10⁹⁸(99-digit number)
19614282219542926789…76926111694652430000
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
1.961 Γ— 10⁹⁸(99-digit number)
19614282219542926789…76926111694652430001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.922 Γ— 10⁹⁸(99-digit number)
39228564439085853578…53852223389304860001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.845 Γ— 10⁹⁸(99-digit number)
78457128878171707157…07704446778609720001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.569 Γ— 10⁹⁹(100-digit number)
15691425775634341431…15408893557219440001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.138 Γ— 10⁹⁹(100-digit number)
31382851551268682862…30817787114438880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.276 Γ— 10⁹⁹(100-digit number)
62765703102537365725…61635574228877760001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.255 Γ— 10¹⁰⁰(101-digit number)
12553140620507473145…23271148457755520001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.510 Γ— 10¹⁰⁰(101-digit number)
25106281241014946290…46542296915511040001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.021 Γ— 10¹⁰⁰(101-digit number)
50212562482029892580…93084593831022080001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.004 Γ— 10¹⁰¹(102-digit number)
10042512496405978516…86169187662044160001
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 279092

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 4d6216f5297dfebdeb45e08126a208c22e2bb58b5efa461d4e0e2755971c16d6

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 #279,092 on Chainz β†—
Circulating Supply:57,771,625 XPMΒ·at block #6,815,938 Β· updates every 60s
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