XPM Prime Explorer symbol
XPMPrime Explorer

Block #74,179

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2013, 9:50:15 AM Β· Difficulty 8.9953 Β· 6,732,692 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b5be0dd68993c864fcec5bacb2a015940fb9b3977b839c449c52262a7c3b094a
View on Chainz β†—

Height

#74,179

Difficulty

8.995335

Transactions

1

Size

201 B

Version

2

Bits

08fece3e

Nonce

31

Timestamp

7/21/2013, 9:50:15 AM

Confirmations

6,732,692

Mined by

⛏️ P2SHANCYL9xhLGasWxPCKGNNvToMvF9WyGnqDE

Merkle Root

a6c75f11b649b26914b147224a23800d2d50933d9fd60cbcd127378b7268a9a0
Transactions (1)
Coinbasea6c75f11b649b2…27378b7268a9a0
1 in β†’ 1 out12.3400 XPM110 B
ANCYL9xh…9WyGnqDE
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.

5.707 Γ— 10⁹⁷(98-digit number)
57074691377406131316…43001926100991962839
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
5.707 Γ— 10⁹⁷(98-digit number)
57074691377406131316…43001926100991962839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.141 Γ— 10⁹⁸(99-digit number)
11414938275481226263…86003852201983925679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.282 Γ— 10⁹⁸(99-digit number)
22829876550962452526…72007704403967851359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.565 Γ— 10⁹⁸(99-digit number)
45659753101924905053…44015408807935702719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.131 Γ— 10⁹⁸(99-digit number)
91319506203849810106…88030817615871405439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.826 Γ— 10⁹⁹(100-digit number)
18263901240769962021…76061635231742810879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.652 Γ— 10⁹⁹(100-digit number)
36527802481539924042…52123270463485621759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.305 Γ— 10⁹⁹(100-digit number)
73055604963079848085…04246540926971243519
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 consecutive prime numbers forming a Cunningham Chain of the First 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,699,075 XPMΒ·at block #6,806,870 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.
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