XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,534,578

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/10/2016, 8:21:41 AM Β· Difficulty 10.6171 Β· 5,282,208 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a71e2bc39fe9650ba95cb53e2533d527b5b89e3215aa592020d4c4f514780c76
View on Chainz β†—

Height

#1,534,578

Difficulty

10.617061

Transactions

2

Size

7.60 KB

Version

2

Bits

0a9df7b3

Nonce

9,551,197

Timestamp

4/10/2016, 8:21:41 AM

Confirmations

5,282,208

Mined by

⛏️ P2SHAf46eBR4Z6JnVH5WXWJSTuHg1PPUUGrtLy

Merkle Root

e0c14f099d310c70093fbc54186cedc23a4444b7c98231dd9eeaf6c0cb27c402
Transactions (2)
Coinbasecebb2d8ba5d5a8…d2c0e094f8741f
1 in β†’ 1 out8.9400 XPM109 B
Af46eBR4…PUUGrtLy
dd303a10b627ee…9c48e63c87d0de
51 in β†’ 1 out608.9648 XPM7.41 KB
AcNzPC4T…FWtxrj38
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.

3.444 Γ— 10⁹⁢(97-digit number)
34449872367121316224…48314920305436876801
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
3.444 Γ— 10⁹⁢(97-digit number)
34449872367121316224…48314920305436876801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.889 Γ— 10⁹⁢(97-digit number)
68899744734242632448…96629840610873753601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.377 Γ— 10⁹⁷(98-digit number)
13779948946848526489…93259681221747507201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.755 Γ— 10⁹⁷(98-digit number)
27559897893697052979…86519362443495014401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.511 Γ— 10⁹⁷(98-digit number)
55119795787394105959…73038724886990028801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.102 Γ— 10⁹⁸(99-digit number)
11023959157478821191…46077449773980057601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.204 Γ— 10⁹⁸(99-digit number)
22047918314957642383…92154899547960115201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.409 Γ— 10⁹⁸(99-digit number)
44095836629915284767…84309799095920230401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.819 Γ— 10⁹⁸(99-digit number)
88191673259830569534…68619598191840460801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.763 Γ— 10⁹⁹(100-digit number)
17638334651966113906…37239196383680921601
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:57,778,323 XPMΒ·at block #6,816,785 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