XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,424,259

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/22/2016, 8:02:59 PM Β· Difficulty 10.7741 Β· 5,415,831 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4ef10a42775e94a8469c3b1af92c50c9dda7fed2d0f6d44bd76fe9492135d503
View on Chainz β†—

Height

#1,424,259

Difficulty

10.774069

Transactions

1

Size

200 B

Version

2

Bits

0ac6295d

Nonce

1,146,023,005

Timestamp

1/22/2016, 8:02:59 PM

Confirmations

5,415,831

Mined by

⛏️ P2SHAaBtXZ2ic3VxG5rjFv5ANHDy5EoGtVxSVj

Merkle Root

041f9c1696550012d0f4154452aaea9752ba51d1d5e849118b0995a2e56943c4
Transactions (1)
Coinbase041f9c16965500…0995a2e56943c4
1 in β†’ 1 out8.6000 XPM110 B
AaBtXZ2i…oGtVxSVj
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.

2.625 Γ— 10⁹⁡(96-digit number)
26254691777892029384…75157970226926121601
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
2.625 Γ— 10⁹⁡(96-digit number)
26254691777892029384…75157970226926121601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.250 Γ— 10⁹⁡(96-digit number)
52509383555784058769…50315940453852243201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.050 Γ— 10⁹⁢(97-digit number)
10501876711156811753…00631880907704486401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.100 Γ— 10⁹⁢(97-digit number)
21003753422313623507…01263761815408972801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.200 Γ— 10⁹⁢(97-digit number)
42007506844627247015…02527523630817945601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.401 Γ— 10⁹⁢(97-digit number)
84015013689254494030…05055047261635891201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.680 Γ— 10⁹⁷(98-digit number)
16803002737850898806…10110094523271782401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.360 Γ— 10⁹⁷(98-digit number)
33606005475701797612…20220189046543564801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.721 Γ— 10⁹⁷(98-digit number)
67212010951403595224…40440378093087129601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.344 Γ— 10⁹⁸(99-digit number)
13442402190280719044…80880756186174259201
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:57,965,030 XPMΒ·at block #6,840,089 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.
Privacy PolicyΒ·
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