XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,753,141

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/17/2018, 3:42:24 PM Β· Difficulty 11.6532 Β· 4,090,761 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f93614745da0affacced549b0fa141fcb541a73edf940ea9f19e0efd572c8e71
View on Chainz β†—

Height

#2,753,141

Difficulty

11.653230

Transactions

1

Size

200 B

Version

2

Bits

0ba73a1b

Nonce

695,402,204

Timestamp

7/17/2018, 3:42:24 PM

Confirmations

4,090,761

Mined by

⛏️ P2SHAMiWvQcW6kQXYj2SmRX1YvNpu4xRmmfH6q

Merkle Root

20b3a8b0eb48dad0f86a7031e2ce2ca8a4e537356c618a6a1e15d7f0c8e04bd5
Transactions (1)
Coinbase20b3a8b0eb48da…15d7f0c8e04bd5
1 in β†’ 1 out7.3500 XPM110 B
AMiWvQcW…xRmmfH6q
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.

2.321 Γ— 10⁹⁴(95-digit number)
23219481908951594391…45167556269328354801
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
2.321 Γ— 10⁹⁴(95-digit number)
23219481908951594391…45167556269328354801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.643 Γ— 10⁹⁴(95-digit number)
46438963817903188783…90335112538656709601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.287 Γ— 10⁹⁴(95-digit number)
92877927635806377567…80670225077313419201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.857 Γ— 10⁹⁡(96-digit number)
18575585527161275513…61340450154626838401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.715 Γ— 10⁹⁡(96-digit number)
37151171054322551027…22680900309253676801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.430 Γ— 10⁹⁡(96-digit number)
74302342108645102054…45361800618507353601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.486 Γ— 10⁹⁢(97-digit number)
14860468421729020410…90723601237014707201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.972 Γ— 10⁹⁢(97-digit number)
29720936843458040821…81447202474029414401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.944 Γ— 10⁹⁢(97-digit number)
59441873686916081643…62894404948058828801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.188 Γ— 10⁹⁷(98-digit number)
11888374737383216328…25788809896117657601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.377 Γ— 10⁹⁷(98-digit number)
23776749474766432657…51577619792235315201
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:57,995,587 XPMΒ·at block #6,843,901 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