XPM Prime Explorer symbol
XPMPrime Explorer

Block #75,976

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 8:33:55 PM Β· Difficulty 9.0583 Β· 6,720,534 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
919333c083995e26051c4211528f7333dd32fb8b4deca07147a2ec516e5c5ef3
View on Chainz β†—

Height

#75,976

Difficulty

9.058315

Transactions

1

Size

201 B

Version

2

Bits

090eedbf

Nonce

1,010

Timestamp

7/21/2013, 8:33:55 PM

Confirmations

6,720,534

Mined by

⛏️ P2SHAVQxbFsH6aZpX2pFKM69EEQVEFKG2vYXbz

Merkle Root

3d6f52043c955ae830583d82af071de4f3666aa87ac40cfcc8135c91c8b8fc8a
Transactions (1)
Coinbase3d6f52043c955a…135c91c8b8fc8a
1 in β†’ 1 out12.1700 XPM110 B
AVQxbFsH…KG2vYXbz
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.

1.565 Γ— 10⁹⁸(99-digit number)
15654492112319019431…94521205447204814761
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
1.565 Γ— 10⁹⁸(99-digit number)
15654492112319019431…94521205447204814761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.130 Γ— 10⁹⁸(99-digit number)
31308984224638038862…89042410894409629521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.261 Γ— 10⁹⁸(99-digit number)
62617968449276077725…78084821788819259041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.252 Γ— 10⁹⁹(100-digit number)
12523593689855215545…56169643577638518081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.504 Γ— 10⁹⁹(100-digit number)
25047187379710431090…12339287155277036161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.009 Γ— 10⁹⁹(100-digit number)
50094374759420862180…24678574310554072321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.001 Γ— 10¹⁰⁰(101-digit number)
10018874951884172436…49357148621108144641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.003 Γ— 10¹⁰⁰(101-digit number)
20037749903768344872…98714297242216289281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.007 Γ— 10¹⁰⁰(101-digit number)
40075499807536689744…97428594484432578561
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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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, …
Cross-reference on Chainz Explorer
Circulating Supply:57,616,083 XPMΒ·at block #6,796,509 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