XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,833,076

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2018, 12:16:08 PM Β· Difficulty 11.7148 Β· 4,008,651 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
85edd9dab3bbeac54541ece9313aea8c7d61240697983e5d2c57832fe1b1e6b5
View on Chainz β†—

Height

#2,833,076

Difficulty

11.714752

Transactions

1

Size

198 B

Version

2

Bits

0bb6fa03

Nonce

1,594,379,494

Timestamp

9/10/2018, 12:16:08 PM

Confirmations

4,008,651

Mined by

⛏️ P2SHAeTX269KH5J6cqZsPCfnN8aLV6cckGCe2t

Merkle Root

357ef0029495b60b9c471fcf82e46bec3b55dcbb571fd7539e52884caa2e8613
Transactions (1)
Coinbase357ef0029495b6…52884caa2e8613
1 in β†’ 1 out7.2700 XPM109 B
AeTX269K…cckGCe2t
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.

1.875 Γ— 10⁹³(94-digit number)
18750237119573731327…22535513469407153501
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
1.875 Γ— 10⁹³(94-digit number)
18750237119573731327…22535513469407153501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.750 Γ— 10⁹³(94-digit number)
37500474239147462654…45071026938814307001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.500 Γ— 10⁹³(94-digit number)
75000948478294925309…90142053877628614001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.500 Γ— 10⁹⁴(95-digit number)
15000189695658985061…80284107755257228001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.000 Γ— 10⁹⁴(95-digit number)
30000379391317970123…60568215510514456001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.000 Γ— 10⁹⁴(95-digit number)
60000758782635940247…21136431021028912001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.200 Γ— 10⁹⁡(96-digit number)
12000151756527188049…42272862042057824001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.400 Γ— 10⁹⁡(96-digit number)
24000303513054376099…84545724084115648001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.800 Γ— 10⁹⁡(96-digit number)
48000607026108752198…69091448168231296001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.600 Γ— 10⁹⁡(96-digit number)
96001214052217504396…38182896336462592001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.920 Γ— 10⁹⁢(97-digit number)
19200242810443500879…76365792672925184001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
3.840 Γ— 10⁹⁢(97-digit number)
38400485620887001758…52731585345850368001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,978,197 XPMΒ·at block #6,841,726 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