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Block #911,279

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/26/2015, 11:34:43 PM Β· Difficulty 10.9315 Β· 5,889,451 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
79bcdb4ea5d614dc934d2c1733eac128bc175b72c3bbfdacf0f314b8cdb05cde
View on Chainz β†—

Height

#911,279

Difficulty

10.931477

Transactions

2

Size

1.83 KB

Version

2

Bits

0aee754a

Nonce

745,686,722

Timestamp

1/26/2015, 11:34:43 PM

Confirmations

5,889,451

Merkle Root

6fcd3516c635f62c24d76eda30cde5aaa50f60c9e09e70fef8661658f417a52a
Transactions (2)
Coinbase3264441251fd3c…80a507e43f165f
1 in β†’ 1 out8.3800 XPM116 B
ANSXnLY2…Sd25TjkD
11d857768fa74a…d3ad47e7ded7d1
11 in β†’ 1 out997.9000 XPM1.63 KB
AQ3SuyCM…AmNvneTb
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.

2.419 Γ— 10⁹⁡(96-digit number)
24190215673037971523…68113180181587402000
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
2.419 Γ— 10⁹⁡(96-digit number)
24190215673037971523…68113180181587402001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.838 Γ— 10⁹⁡(96-digit number)
48380431346075943046…36226360363174804001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.676 Γ— 10⁹⁡(96-digit number)
96760862692151886093…72452720726349608001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.935 Γ— 10⁹⁢(97-digit number)
19352172538430377218…44905441452699216001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.870 Γ— 10⁹⁢(97-digit number)
38704345076860754437…89810882905398432001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.740 Γ— 10⁹⁢(97-digit number)
77408690153721508874…79621765810796864001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.548 Γ— 10⁹⁷(98-digit number)
15481738030744301774…59243531621593728001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.096 Γ— 10⁹⁷(98-digit number)
30963476061488603549…18487063243187456001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.192 Γ— 10⁹⁷(98-digit number)
61926952122977207099…36974126486374912001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.238 Γ— 10⁹⁸(99-digit number)
12385390424595441419…73948252972749824001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.477 Γ— 10⁹⁸(99-digit number)
24770780849190882839…47896505945499648001
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 911279

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 79bcdb4ea5d614dc934d2c1733eac128bc175b72c3bbfdacf0f314b8cdb05cde

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 #911,279 on Chainz β†—
Circulating Supply:57,649,910 XPMΒ·at block #6,800,729 Β· updates every 60s
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