XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,612,191

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/3/2016, 9:40:15 AM Β· Difficulty 10.6032 Β· 5,226,648 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dfc3d54f2da4cf324647546b6f775f9d77478f38cc9a86418e11b0d3be451b58
View on Chainz β†—

Height

#1,612,191

Difficulty

10.603202

Transactions

1

Size

199 B

Version

2

Bits

0a9a6b75

Nonce

491,865,469

Timestamp

6/3/2016, 9:40:15 AM

Confirmations

5,226,648

Mined by

⛏️ P2SHAWTX6373Z4693ui22BphPHhTGnQadNVHj7

Merkle Root

77dec6d4653aa5eabc669219a94ecdadcad38e4b1661be219d45db41ea464ab6
Transactions (1)
Coinbase77dec6d4653aa5…45db41ea464ab6
1 in β†’ 1 out8.8800 XPM109 B
AWTX6373…QadNVHj7
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.

4.956 Γ— 10⁹⁡(96-digit number)
49560805920016719597…37069236371764469761
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
4.956 Γ— 10⁹⁡(96-digit number)
49560805920016719597…37069236371764469761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.912 Γ— 10⁹⁡(96-digit number)
99121611840033439194…74138472743528939521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.982 Γ— 10⁹⁢(97-digit number)
19824322368006687838…48276945487057879041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.964 Γ— 10⁹⁢(97-digit number)
39648644736013375677…96553890974115758081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.929 Γ— 10⁹⁢(97-digit number)
79297289472026751355…93107781948231516161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.585 Γ— 10⁹⁷(98-digit number)
15859457894405350271…86215563896463032321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.171 Γ— 10⁹⁷(98-digit number)
31718915788810700542…72431127792926064641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.343 Γ— 10⁹⁷(98-digit number)
63437831577621401084…44862255585852129281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.268 Γ— 10⁹⁸(99-digit number)
12687566315524280216…89724511171704258561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.537 Γ— 10⁹⁸(99-digit number)
25375132631048560433…79449022343408517121
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:57,954,974 XPMΒ·at block #6,838,838 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