XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #73,163

Block #73,163

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 4:18:36 AM Β· Difficulty 8.9946 Β· 6,727,592 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
708fc1d1b40a858bda7dc595f6166d04273fefe6ede21cba2f7e3e6fcf8ed3a0
View on Chainz β†—

Height

#73,163

Difficulty

8.994623

Transactions

1

Size

199 B

Version

2

Bits

08fe9f9f

Nonce

65

Timestamp

7/21/2013, 4:18:36 AM

Confirmations

6,727,592

Merkle Root

7b1ad7c9d68b8bbc51feda710332b7f8c88188c372d4e7b3ea59dca5716b66c9
Transactions (1)
Coinbase7b1ad7c9d68b8b…59dca5716b66c9
1 in β†’ 1 out12.3400 XPM109 B
APuKQSxs…5YJgufZx
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.

1.019 Γ— 10⁹⁡(96-digit number)
10199056455197050222…30109761642201781400
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
1.019 Γ— 10⁹⁡(96-digit number)
10199056455197050222…30109761642201781401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.039 Γ— 10⁹⁡(96-digit number)
20398112910394100444…60219523284403562801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.079 Γ— 10⁹⁡(96-digit number)
40796225820788200888…20439046568807125601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.159 Γ— 10⁹⁡(96-digit number)
81592451641576401777…40878093137614251201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.631 Γ— 10⁹⁢(97-digit number)
16318490328315280355…81756186275228502401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.263 Γ— 10⁹⁢(97-digit number)
32636980656630560710…63512372550457004801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.527 Γ— 10⁹⁢(97-digit number)
65273961313261121421…27024745100914009601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.305 Γ— 10⁹⁷(98-digit number)
13054792262652224284…54049490201828019201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.610 Γ— 10⁹⁷(98-digit number)
26109584525304448568…08098980403656038401
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 73163

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 708fc1d1b40a858bda7dc595f6166d04273fefe6ede21cba2f7e3e6fcf8ed3a0

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 #73,163 on Chainz β†—
Circulating Supply:57,650,110 XPMΒ·at block #6,800,754 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK