XPM Prime Explorer symbol
XPMPrime Explorer

Block #241,888

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/3/2013, 11:23:35 AM Β· Difficulty 9.9586 Β· 6,560,623 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4a45b4c638380d326598fb1d404534bf8fbc70f84994dd2a598106e01a60e216
View on Chainz β†—

Height

#241,888

Difficulty

9.958638

Transactions

1

Size

198 B

Version

2

Bits

09f5694a

Nonce

322,868

Timestamp

11/3/2013, 11:23:35 AM

Confirmations

6,560,623

Mined by

⛏️ P2SHAZz6Bg87J8VhAYyRKDwNgf7vf5MZtiQn8U

Merkle Root

4c782fb48f568b74c542c721ef7d2d366c70bce9e4775f8097c5e90330cdbcd4
Transactions (1)
Coinbase4c782fb48f568b…c5e90330cdbcd4
1 in β†’ 1 out10.0700 XPM109 B
AZz6Bg87…MZtiQn8U
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.

9.343 Γ— 10⁹²(93-digit number)
93430835902917582427…10932172660492666881
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
9.343 Γ— 10⁹²(93-digit number)
93430835902917582427…10932172660492666881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.868 Γ— 10⁹³(94-digit number)
18686167180583516485…21864345320985333761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.737 Γ— 10⁹³(94-digit number)
37372334361167032971…43728690641970667521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.474 Γ— 10⁹³(94-digit number)
74744668722334065942…87457381283941335041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.494 Γ— 10⁹⁴(95-digit number)
14948933744466813188…74914762567882670081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.989 Γ— 10⁹⁴(95-digit number)
29897867488933626376…49829525135765340161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.979 Γ— 10⁹⁴(95-digit number)
59795734977867252753…99659050271530680321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.195 Γ— 10⁹⁡(96-digit number)
11959146995573450550…99318100543061360641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.391 Γ— 10⁹⁡(96-digit number)
23918293991146901101…98636201086122721281
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:57,664,096 XPMΒ·at block #6,802,510 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