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Block #177,007

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/23/2013, 8:39:00 AM Β· Difficulty 9.8652 Β· 6,619,405 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
98c7bb1e146ddb0cfbe97e6ad94becc7aac561f06ff613b5e97cb03bb1c8a62b
View on Chainz β†—

Height

#177,007

Difficulty

9.865158

Transactions

1

Size

200 B

Version

2

Bits

09dd7af9

Nonce

49,612

Timestamp

9/23/2013, 8:39:00 AM

Confirmations

6,619,405

Merkle Root

8664255bbda1d3076cb45610f4de0591c971be7cd6adced3f325340a8d13de50
Transactions (1)
Coinbase8664255bbda1d3…25340a8d13de50
1 in β†’ 1 out10.2600 XPM109 B
AVTMAkKp…XEYDe3mD
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.

2.177 Γ— 10⁹⁷(98-digit number)
21776598879932540160…71739254347559911640
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.177 Γ— 10⁹⁷(98-digit number)
21776598879932540160…71739254347559911639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.355 Γ— 10⁹⁷(98-digit number)
43553197759865080320…43478508695119823279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.710 Γ— 10⁹⁷(98-digit number)
87106395519730160640…86957017390239646559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.742 Γ— 10⁹⁸(99-digit number)
17421279103946032128…73914034780479293119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.484 Γ— 10⁹⁸(99-digit number)
34842558207892064256…47828069560958586239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.968 Γ— 10⁹⁸(99-digit number)
69685116415784128512…95656139121917172479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.393 Γ— 10⁹⁹(100-digit number)
13937023283156825702…91312278243834344959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.787 Γ— 10⁹⁹(100-digit number)
27874046566313651405…82624556487668689919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.574 Γ— 10⁹⁹(100-digit number)
55748093132627302810…65249112975337379839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First 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
CommonChain length 9
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 177007

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 98c7bb1e146ddb0cfbe97e6ad94becc7aac561f06ff613b5e97cb03bb1c8a62b

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 #177,007 on Chainz β†—
Circulating Supply:57,615,284 XPMΒ·at block #6,796,411 Β· updates every 60s
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