XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,131,420

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/25/2017, 2:23:38 AM Β· Difficulty 10.9101 Β· 4,708,211 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cbbfaccd2e4a18539eeb8c47ee768365e105debd3c86eb82c88ac7c0379f4b10
View on Chainz β†—

Height

#2,131,420

Difficulty

10.910142

Transactions

2

Size

426 B

Version

2

Bits

0ae8ff11

Nonce

1,872,604,744

Timestamp

5/25/2017, 2:23:38 AM

Confirmations

4,708,211

Mined by

⛏️ P2SHAWN44qSm1842Mx1wvkKQwc67q76NGHh634

Merkle Root

09d9fa7cd456bcb0fd052dd444638e048d845adc05e60bc0a5cc186de41f80d0
Transactions (2)
Coinbase9bc8d18196f47a…c7d76d7ddf15da
1 in β†’ 1 out8.4000 XPM110 B
AWN44qSm…6NGHh634
312af9a857cc72…7de9ad2096e98c
1 in β†’ 2 out5765.3496 XPM226 B
APe7MFxP…LWenBVYtAJvxmec3…xoY5kW5s
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.

5.415 Γ— 10⁹³(94-digit number)
54153126256481992530…50665480238220279201
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
5.415 Γ— 10⁹³(94-digit number)
54153126256481992530…50665480238220279201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.083 Γ— 10⁹⁴(95-digit number)
10830625251296398506…01330960476440558401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.166 Γ— 10⁹⁴(95-digit number)
21661250502592797012…02661920952881116801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.332 Γ— 10⁹⁴(95-digit number)
43322501005185594024…05323841905762233601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.664 Γ— 10⁹⁴(95-digit number)
86645002010371188048…10647683811524467201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.732 Γ— 10⁹⁡(96-digit number)
17329000402074237609…21295367623048934401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.465 Γ— 10⁹⁡(96-digit number)
34658000804148475219…42590735246097868801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.931 Γ— 10⁹⁡(96-digit number)
69316001608296950438…85181470492195737601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.386 Γ— 10⁹⁢(97-digit number)
13863200321659390087…70362940984391475201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.772 Γ— 10⁹⁢(97-digit number)
27726400643318780175…40725881968782950401
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:57,961,341 XPMΒ·at block #6,839,630 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