XPM Prime Explorer symbol
XPMPrime Explorer

Block #588,231

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/14/2014, 11:54:01 AM Β· Difficulty 10.9498 Β· 6,219,686 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e310da92f3d4660253e0f75c8f78d503543348926acde344c451d0041744fb5c
View on Chainz β†—

Height

#588,231

Difficulty

10.949771

Transactions

2

Size

434 B

Version

2

Bits

0af3242b

Nonce

345,125,458

Timestamp

6/14/2014, 11:54:01 AM

Confirmations

6,219,686

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ea37a8049b0c3ba7d5a9b37f606104ab4c0daf2238d8095fd5b63e730cb100f0
Transactions (2)
Coinbasea7d80fdad1255e…18d22d7b883761
1 in β†’ 1 out8.3400 XPM116 B
ANSXnLY2…Sd25TjkD
ed028f7b800ba7…537b1c18bd68c3
1 in β†’ 2 out5.5724 XPM226 B
AcB1Cdou…cFjow1c5AYfFg4Jq…3TJQsysp
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.

1.923 Γ— 10⁹⁸(99-digit number)
19236424761424943079…74083678085702596001
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
1.923 Γ— 10⁹⁸(99-digit number)
19236424761424943079…74083678085702596001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.847 Γ— 10⁹⁸(99-digit number)
38472849522849886159…48167356171405192001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.694 Γ— 10⁹⁸(99-digit number)
76945699045699772318…96334712342810384001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.538 Γ— 10⁹⁹(100-digit number)
15389139809139954463…92669424685620768001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.077 Γ— 10⁹⁹(100-digit number)
30778279618279908927…85338849371241536001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.155 Γ— 10⁹⁹(100-digit number)
61556559236559817854…70677698742483072001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.231 Γ— 10¹⁰⁰(101-digit number)
12311311847311963570…41355397484966144001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.462 Γ— 10¹⁰⁰(101-digit number)
24622623694623927141…82710794969932288001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.924 Γ— 10¹⁰⁰(101-digit number)
49245247389247854283…65421589939864576001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.849 Γ— 10¹⁰⁰(101-digit number)
98490494778495708567…30843179879729152001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,707,371 XPMΒ·at block #6,807,916 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

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy