XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,799,480

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/18/2018, 2:52:38 PM Β· Difficulty 11.6754 Β· 4,042,075 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a53e7daa255d3b40a1270ed171471dbf33c07fc221b8f27b22f2f2b310e19ba2
View on Chainz β†—

Height

#2,799,480

Difficulty

11.675438

Transactions

2

Size

574 B

Version

2

Bits

0bace97a

Nonce

997,791,653

Timestamp

8/18/2018, 2:52:38 PM

Confirmations

4,042,075

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

472aefb70e77930c0347334cff8f98e9ff89935ff2baabafb795442988769550
Transactions (2)
Coinbasebe32e75f57551f…5541b58f9b59da
1 in β†’ 1 out7.3300 XPM110 B
AZtxQr2F…7grUWrUz
f272865bf369f0…d12379bb082e2e
2 in β†’ 2 out5.3381 XPM374 B
AYv8bFdF…5hZLWYPcAPA6HLp2…dkyt53Hu
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.

1.936 Γ— 10⁹⁡(96-digit number)
19364253405544309592…51578549339670048401
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
1.936 Γ— 10⁹⁡(96-digit number)
19364253405544309592…51578549339670048401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.872 Γ— 10⁹⁡(96-digit number)
38728506811088619184…03157098679340096801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.745 Γ— 10⁹⁡(96-digit number)
77457013622177238368…06314197358680193601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.549 Γ— 10⁹⁢(97-digit number)
15491402724435447673…12628394717360387201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.098 Γ— 10⁹⁢(97-digit number)
30982805448870895347…25256789434720774401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.196 Γ— 10⁹⁢(97-digit number)
61965610897741790695…50513578869441548801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.239 Γ— 10⁹⁷(98-digit number)
12393122179548358139…01027157738883097601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.478 Γ— 10⁹⁷(98-digit number)
24786244359096716278…02054315477766195201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.957 Γ— 10⁹⁷(98-digit number)
49572488718193432556…04108630955532390401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.914 Γ— 10⁹⁷(98-digit number)
99144977436386865112…08217261911064780801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.982 Γ— 10⁹⁸(99-digit number)
19828995487277373022…16434523822129561601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,976,825 XPMΒ·at block #6,841,554 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