XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,087,956

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/3/2015, 7:48:06 AM Β· Difficulty 10.7520 Β· 5,724,449 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
57dfbdc8deceae1c1770150b8d899ac216709b118a38573769d1b5646192efb0
View on Chainz β†—

Height

#1,087,956

Difficulty

10.751966

Transactions

1

Size

200 B

Version

2

Bits

0ac080d3

Nonce

244,456,978

Timestamp

6/3/2015, 7:48:06 AM

Confirmations

5,724,449

Mined by

⛏️ P2SHANCZAhFAbKSZQtiaCEE6qAhDsq4XJ8NSvi

Merkle Root

8e10e5cb588b9098853d954683bfbb3018085e3dea4564198470a0319e4ef18c
Transactions (1)
Coinbase8e10e5cb588b90…70a0319e4ef18c
1 in β†’ 1 out8.6400 XPM109 B
ANCZAhFA…4XJ8NSvi
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.

1.434 Γ— 10⁹⁷(98-digit number)
14348705183974580638…32740947538538462081
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
1.434 Γ— 10⁹⁷(98-digit number)
14348705183974580638…32740947538538462081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.869 Γ— 10⁹⁷(98-digit number)
28697410367949161277…65481895077076924161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.739 Γ— 10⁹⁷(98-digit number)
57394820735898322554…30963790154153848321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.147 Γ— 10⁹⁸(99-digit number)
11478964147179664510…61927580308307696641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.295 Γ— 10⁹⁸(99-digit number)
22957928294359329021…23855160616615393281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.591 Γ— 10⁹⁸(99-digit number)
45915856588718658043…47710321233230786561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.183 Γ— 10⁹⁸(99-digit number)
91831713177437316087…95420642466461573121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.836 Γ— 10⁹⁹(100-digit number)
18366342635487463217…90841284932923146241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.673 Γ— 10⁹⁹(100-digit number)
36732685270974926434…81682569865846292481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.346 Γ— 10⁹⁹(100-digit number)
73465370541949852869…63365139731692584961
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:57,743,266 XPMΒ·at block #6,812,404 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