XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,165,937

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/18/2017, 12:46:05 PM Β· Difficulty 10.8985 Β· 4,651,693 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
154357a73303e094b96704e7f0b31e6c404dedfc4f36db33d6df3465fd8b08d8
View on Chainz β†—

Height

#2,165,937

Difficulty

10.898537

Transactions

2

Size

1.25 KB

Version

2

Bits

0ae60683

Nonce

472,658,462

Timestamp

6/18/2017, 12:46:05 PM

Confirmations

4,651,693

Mined by

⛏️ P2SHAWohQLx5RYgHgdCF32P2FTEE9gGDZ3HQCf

Merkle Root

bf69db522e8f8af069fa149183d00b751f883d704e464cab8e43be90bf593187
Transactions (2)
Coinbase910d99dcc675e3…ad64d1ccd75719
1 in β†’ 1 out8.4300 XPM110 B
AWohQLx5…GDZ3HQCf
7ac867f4017b21…0795467c792368
7 in β†’ 1 out140.0621 XPM1.05 KB
AJT5ZDj4…DtnSSE5g
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.

6.605 Γ— 10⁹⁢(97-digit number)
66051794647483852727…69644455034499522561
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
6.605 Γ— 10⁹⁢(97-digit number)
66051794647483852727…69644455034499522561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.321 Γ— 10⁹⁷(98-digit number)
13210358929496770545…39288910068999045121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.642 Γ— 10⁹⁷(98-digit number)
26420717858993541091…78577820137998090241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.284 Γ— 10⁹⁷(98-digit number)
52841435717987082182…57155640275996180481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.056 Γ— 10⁹⁸(99-digit number)
10568287143597416436…14311280551992360961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.113 Γ— 10⁹⁸(99-digit number)
21136574287194832872…28622561103984721921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.227 Γ— 10⁹⁸(99-digit number)
42273148574389665745…57245122207969443841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.454 Γ— 10⁹⁸(99-digit number)
84546297148779331491…14490244415938887681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.690 Γ— 10⁹⁹(100-digit number)
16909259429755866298…28980488831877775361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.381 Γ— 10⁹⁹(100-digit number)
33818518859511732596…57960977663755550721
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:57,785,092 XPMΒ·at block #6,817,629 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