XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,038,723

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2015, 8:10:12 AM Β· Difficulty 10.7352 Β· 5,776,261 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
72fadb90fa509fcccaecd08f76f8cbe9329beb8143e7c264594d51d2cbee13ab
View on Chainz β†—

Height

#1,038,723

Difficulty

10.735220

Transactions

2

Size

434 B

Version

2

Bits

0abc3764

Nonce

1,516,776,632

Timestamp

4/30/2015, 8:10:12 AM

Confirmations

5,776,261

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

99305e790d87038bf6b9d9b7530d54044e85dcf0e23e0e090200f3aa2728956b
Transactions (2)
Coinbasec0d33b671950d4…8c47a58c2de02a
1 in β†’ 1 out8.6700 XPM116 B
ANSXnLY2…Sd25TjkD
1e367cf239e2d9…40d2e8fe5619dc
1 in β†’ 2 out1.3065 XPM227 B
AH9HenSr…7F72AXruASAbhU1S…nMvsgkL5
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.

2.944 Γ— 10⁹⁢(97-digit number)
29448040543661140238…78041576684496440321
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
2.944 Γ— 10⁹⁢(97-digit number)
29448040543661140238…78041576684496440321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.889 Γ— 10⁹⁢(97-digit number)
58896081087322280477…56083153368992880641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.177 Γ— 10⁹⁷(98-digit number)
11779216217464456095…12166306737985761281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.355 Γ— 10⁹⁷(98-digit number)
23558432434928912190…24332613475971522561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.711 Γ— 10⁹⁷(98-digit number)
47116864869857824381…48665226951943045121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.423 Γ— 10⁹⁷(98-digit number)
94233729739715648763…97330453903886090241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.884 Γ— 10⁹⁸(99-digit number)
18846745947943129752…94660907807772180481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.769 Γ— 10⁹⁸(99-digit number)
37693491895886259505…89321815615544360961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.538 Γ— 10⁹⁸(99-digit number)
75386983791772519010…78643631231088721921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.507 Γ— 10⁹⁹(100-digit number)
15077396758354503802…57287262462177443841
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:57,763,956 XPMΒ·at block #6,814,983 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