XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,348,693

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/30/2015, 12:39:36 PM Β· Difficulty 10.8192 Β· 5,477,882 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1d442a98f09af224a5c04d7e46a821d74f35208c414f4be8878f049825323b75
View on Chainz β†—

Height

#1,348,693

Difficulty

10.819186

Transactions

2

Size

7.20 KB

Version

2

Bits

0ad1b62a

Nonce

278,305,832

Timestamp

11/30/2015, 12:39:36 PM

Confirmations

5,477,882

Mined by

⛏️ P2SHAJZdma72BbjGbHogdmyaPrxfQUKhrRQsft

Merkle Root

2bcc82539732f3b6f5f8211f565485ea5fe6e6c2b079e8ae55fe80a42791a6b3
Transactions (2)
Coinbasea934289a83a5ba…7ba7e61dd59a24
1 in β†’ 1 out8.6100 XPM109 B
AJZdma72…KhrRQsft
7e31b5d6600d21…0751bf956c75d5
48 in β†’ 2 out33.7446 XPM7.00 KB
AbecWDS9…1vtToSMLAaot2Hsd…CAMci8xv
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.

5.869 Γ— 10⁹⁡(96-digit number)
58691554989098202613…37955013976982231041
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
5.869 Γ— 10⁹⁡(96-digit number)
58691554989098202613…37955013976982231041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.173 Γ— 10⁹⁢(97-digit number)
11738310997819640522…75910027953964462081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.347 Γ— 10⁹⁢(97-digit number)
23476621995639281045…51820055907928924161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.695 Γ— 10⁹⁢(97-digit number)
46953243991278562090…03640111815857848321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.390 Γ— 10⁹⁢(97-digit number)
93906487982557124181…07280223631715696641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.878 Γ— 10⁹⁷(98-digit number)
18781297596511424836…14560447263431393281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.756 Γ— 10⁹⁷(98-digit number)
37562595193022849672…29120894526862786561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.512 Γ— 10⁹⁷(98-digit number)
75125190386045699345…58241789053725573121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.502 Γ— 10⁹⁸(99-digit number)
15025038077209139869…16483578107451146241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.005 Γ— 10⁹⁸(99-digit number)
30050076154418279738…32967156214902292481
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:57,856,749 XPMΒ·at block #6,826,574 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