XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #73,156

Block #73,156

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2013, 4:16:34 AM Β· Difficulty 8.9946 Β· 6,721,256 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aa00ba3fac4a17fa32bf9edc8baf3cb0447c1b9095539c4ee4c55b59ea8fd92b
View on Chainz β†—

Height

#73,156

Difficulty

8.994618

Transactions

1

Size

200 B

Version

2

Bits

08fe9f4e

Nonce

349

Timestamp

7/21/2013, 4:16:34 AM

Confirmations

6,721,256

Merkle Root

a1535200949069f7b9170495d8db84aae7433b3d678c97edac6ded6a38df90ac
Transactions (1)
Coinbasea1535200949069…6ded6a38df90ac
1 in β†’ 1 out12.3400 XPM110 B
AQsYp9dj…q6VmbREc
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.

6.531 Γ— 10⁹⁴(95-digit number)
65318236316148308395…58544204820601050600
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
6.531 Γ— 10⁹⁴(95-digit number)
65318236316148308395…58544204820601050599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.306 Γ— 10⁹⁡(96-digit number)
13063647263229661679…17088409641202101199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.612 Γ— 10⁹⁡(96-digit number)
26127294526459323358…34176819282404202399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.225 Γ— 10⁹⁡(96-digit number)
52254589052918646716…68353638564808404799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.045 Γ— 10⁹⁢(97-digit number)
10450917810583729343…36707277129616809599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.090 Γ— 10⁹⁢(97-digit number)
20901835621167458686…73414554259233619199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.180 Γ— 10⁹⁢(97-digit number)
41803671242334917373…46829108518467238399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.360 Γ— 10⁹⁢(97-digit number)
83607342484669834746…93658217036934476799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.672 Γ— 10⁹⁷(98-digit number)
16721468496933966949…87316434073868953599
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 73156

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 aa00ba3fac4a17fa32bf9edc8baf3cb0447c1b9095539c4ee4c55b59ea8fd92b

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 #73,156 on Chainz β†—
Circulating Supply:57,599,329 XPMΒ·at block #6,794,411 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