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Block #779,546

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/23/2014, 1:31:20 AM Β· Difficulty 10.9779 Β· 6,047,186 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b0f2381afd65e0e4200dd6c398fcffc27584658669b312d0f9abe7c0af850c0b
View on Chainz β†—

Height

#779,546

Difficulty

10.977884

Transactions

1

Size

207 B

Version

2

Bits

0afa569b

Nonce

144,981,810

Timestamp

10/23/2014, 1:31:20 AM

Confirmations

6,047,186

Merkle Root

cc62d30ce663b6d8349b27d288ca66c41b925822be0fe4574800d0d6fcb7f991
Transactions (1)
Coinbasecc62d30ce663b6…00d0d6fcb7f991
1 in β†’ 1 out8.2800 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.

2.295 Γ— 10⁹⁷(98-digit number)
22953583593358029187…64322382559315066880
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
2.295 Γ— 10⁹⁷(98-digit number)
22953583593358029187…64322382559315066881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.590 Γ— 10⁹⁷(98-digit number)
45907167186716058374…28644765118630133761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.181 Γ— 10⁹⁷(98-digit number)
91814334373432116748…57289530237260267521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.836 Γ— 10⁹⁸(99-digit number)
18362866874686423349…14579060474520535041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.672 Γ— 10⁹⁸(99-digit number)
36725733749372846699…29158120949041070081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.345 Γ— 10⁹⁸(99-digit number)
73451467498745693399…58316241898082140161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.469 Γ— 10⁹⁹(100-digit number)
14690293499749138679…16632483796164280321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.938 Γ— 10⁹⁹(100-digit number)
29380586999498277359…33264967592328560641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.876 Γ— 10⁹⁹(100-digit number)
58761173998996554719…66529935184657121281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.175 Γ— 10¹⁰⁰(101-digit number)
11752234799799310943…33059870369314242561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.350 Γ— 10¹⁰⁰(101-digit number)
23504469599598621887…66119740738628485121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
4.700 Γ— 10¹⁰⁰(101-digit number)
47008939199197243775…32239481477256970241
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 779546

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 b0f2381afd65e0e4200dd6c398fcffc27584658669b312d0f9abe7c0af850c0b

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 #779,546 on Chainz β†—
Circulating Supply:57,858,010 XPMΒ·at block #6,826,731 Β· updates every 60s
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