XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #81,172

Block #81,172

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/24/2013, 2:29:58 PM Β· Difficulty 9.2646 Β· 6,718,830 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
735b7fec3a88ca350a21ca341b013be012b2ee4fa7b9dd2f27851709f0f6549a
View on Chainz β†—

Height

#81,172

Difficulty

9.264561

Transactions

1

Size

200 B

Version

2

Bits

0943ba40

Nonce

81,021

Timestamp

7/24/2013, 2:29:58 PM

Confirmations

6,718,830

Merkle Root

154abdef612aef4fb4b4dcba171984805e5c7ac736953317e143a88544c0fc14
Transactions (1)
Coinbase154abdef612aef…43a88544c0fc14
1 in β†’ 1 out11.6300 XPM109 B
Aac34gpk…SatG1BeY
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.

1.201 Γ— 10⁹⁸(99-digit number)
12015337052150027363…12545433986939971800
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
1.201 Γ— 10⁹⁸(99-digit number)
12015337052150027363…12545433986939971801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.403 Γ— 10⁹⁸(99-digit number)
24030674104300054727…25090867973879943601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.806 Γ— 10⁹⁸(99-digit number)
48061348208600109455…50181735947759887201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.612 Γ— 10⁹⁸(99-digit number)
96122696417200218911…00363471895519774401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.922 Γ— 10⁹⁹(100-digit number)
19224539283440043782…00726943791039548801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.844 Γ— 10⁹⁹(100-digit number)
38449078566880087564…01453887582079097601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.689 Γ— 10⁹⁹(100-digit number)
76898157133760175128…02907775164158195201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.537 Γ— 10¹⁰⁰(101-digit number)
15379631426752035025…05815550328316390401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.075 Γ— 10¹⁰⁰(101-digit number)
30759262853504070051…11631100656632780801
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 81172

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 735b7fec3a88ca350a21ca341b013be012b2ee4fa7b9dd2f27851709f0f6549a

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 #81,172 on Chainz β†—
Circulating Supply:57,644,072 XPMΒ·at block #6,800,001 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