XPM Prime Explorer symbol
XPMPrime Explorer

Block #180,702

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/26/2013, 12:18:07 AM Β· Difficulty 9.8620 Β· 6,615,495 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1ef59eaf9a355ac6107367c574a1e3804e56cd21092e56b7ae4368bd1fabaea0
View on Chainz β†—

Height

#180,702

Difficulty

9.861974

Transactions

1

Size

199 B

Version

2

Bits

09dcaa5b

Nonce

20,417

Timestamp

9/26/2013, 12:18:07 AM

Confirmations

6,615,495

Mined by

⛏️ P2SHAWsEijaAmPVVY4otUbJH1Yqtdf9WbDL6tH

Merkle Root

62ee680b8f8135d7a046f916b868509777a6083cf021e758df4d7818468fa90f
Transactions (1)
Coinbase62ee680b8f8135…4d7818468fa90f
1 in β†’ 1 out10.2700 XPM109 B
AWsEijaA…9WbDL6tH
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.

5.731 Γ— 10⁹³(94-digit number)
57315330425649863843…79155313028572875499
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
5.731 Γ— 10⁹³(94-digit number)
57315330425649863843…79155313028572875499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.146 Γ— 10⁹⁴(95-digit number)
11463066085129972768…58310626057145750999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.292 Γ— 10⁹⁴(95-digit number)
22926132170259945537…16621252114291501999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.585 Γ— 10⁹⁴(95-digit number)
45852264340519891074…33242504228583003999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.170 Γ— 10⁹⁴(95-digit number)
91704528681039782149…66485008457166007999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.834 Γ— 10⁹⁡(96-digit number)
18340905736207956429…32970016914332015999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.668 Γ— 10⁹⁡(96-digit number)
36681811472415912859…65940033828664031999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.336 Γ— 10⁹⁡(96-digit number)
73363622944831825719…31880067657328063999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.467 Γ— 10⁹⁢(97-digit number)
14672724588966365143…63760135314656127999
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.

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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,613,576 XPMΒ·at block #6,796,196 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