XPM Prime Explorer symbol
XPMPrime Explorer

Block #198,213

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/7/2013, 2:57:57 PM Β· Difficulty 9.8847 Β· 6,597,878 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7479508072b27b27036ff6cdca1dfd43c4f578d65b4ac8ce9d1cfebea9327bed
View on Chainz β†—

Height

#198,213

Difficulty

9.884660

Transactions

1

Size

206 B

Version

2

Bits

09e27919

Nonce

16,779,521

Timestamp

10/7/2013, 2:57:57 PM

Confirmations

6,597,878

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

f8c3617b2bf457ec0202f485acc5e04eea71c43a1293bd8f0588e798de62d484
Transactions (1)
Coinbasef8c3617b2bf457…88e798de62d484
1 in β†’ 1 out10.2200 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.487 Γ— 10⁹⁡(96-digit number)
14872085149808579977…53971845845525058939
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
1.487 Γ— 10⁹⁡(96-digit number)
14872085149808579977…53971845845525058939
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.974 Γ— 10⁹⁡(96-digit number)
29744170299617159955…07943691691050117879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.948 Γ— 10⁹⁡(96-digit number)
59488340599234319910…15887383382100235759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.189 Γ— 10⁹⁢(97-digit number)
11897668119846863982…31774766764200471519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.379 Γ— 10⁹⁢(97-digit number)
23795336239693727964…63549533528400943039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.759 Γ— 10⁹⁢(97-digit number)
47590672479387455928…27099067056801886079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.518 Γ— 10⁹⁢(97-digit number)
95181344958774911857…54198134113603772159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.903 Γ— 10⁹⁷(98-digit number)
19036268991754982371…08396268227207544319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.807 Γ— 10⁹⁷(98-digit number)
38072537983509964742…16792536454415088639
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:57,612,727 XPMΒ·at block #6,796,090 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