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Block #173,132

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/20/2013, 6:30:30 PM Β· Difficulty 9.8610 Β· 6,639,175 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
706de01ea91a13c0a777a38b6d036afa526e8e8becf261b4f32b649aa4edfcb5
View on Chainz β†—

Height

#173,132

Difficulty

9.860989

Transactions

2

Size

391 B

Version

2

Bits

09dc69c9

Nonce

108,271

Timestamp

9/20/2013, 6:30:30 PM

Confirmations

6,639,175

Merkle Root

ba47743b54c7da93b7ed1f422f486e1a64e6046f6102843e458d5c16b81d03e1
Transactions (2)
Coinbase7381fa306825a4…643f1372890697
1 in β†’ 1 out10.2800 XPM109 B
AKvL3reY…pP6LXY9G
aa9bfe669adc7d…ccd888b5be80b1
1 in β†’ 2 out10.2600 XPM192 B
AFz9fXym…wh4UqpkLAKEti8Ns…1SGFYXBt
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.

2.874 Γ— 10⁹⁴(95-digit number)
28749517312827466989…52729584290690926080
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
2.874 Γ— 10⁹⁴(95-digit number)
28749517312827466989…52729584290690926081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.749 Γ— 10⁹⁴(95-digit number)
57499034625654933979…05459168581381852161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.149 Γ— 10⁹⁡(96-digit number)
11499806925130986795…10918337162763704321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.299 Γ— 10⁹⁡(96-digit number)
22999613850261973591…21836674325527408641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.599 Γ— 10⁹⁡(96-digit number)
45999227700523947183…43673348651054817281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.199 Γ— 10⁹⁡(96-digit number)
91998455401047894367…87346697302109634561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.839 Γ— 10⁹⁢(97-digit number)
18399691080209578873…74693394604219269121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.679 Γ— 10⁹⁢(97-digit number)
36799382160419157746…49386789208438538241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.359 Γ— 10⁹⁢(97-digit number)
73598764320838315493…98773578416877076481
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 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
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 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 173132

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 706de01ea91a13c0a777a38b6d036afa526e8e8becf261b4f32b649aa4edfcb5

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 #173,132 on Chainz β†—
Circulating Supply:57,742,470 XPMΒ·at block #6,812,306 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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