XPM Prime Explorer symbol
XPMPrime Explorer

Block #472,179

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/3/2014, 2:45:59 AM Β· Difficulty 10.4337 Β· 6,335,757 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
897b82874dfc10f0561191c164c2e4d38c77f0dfc316b84f1d98291319a2a55e
View on Chainz β†—

Height

#472,179

Difficulty

10.433709

Transactions

1

Size

201 B

Version

2

Bits

0a6f0794

Nonce

19,259

Timestamp

4/3/2014, 2:45:59 AM

Confirmations

6,335,757

Mined by

⛏️ P2SHAb64gm8KUnFNR9oWChHpwHnuPjmwRnN1CH

Merkle Root

93938397e70c2f6a070d982f46dd13cdac7749f97316233c2979877ff8ff9547
Transactions (1)
Coinbase93938397e70c2f…79877ff8ff9547
1 in β†’ 1 out9.1700 XPM109 B
Ab64gm8K…mwRnN1CH
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.

3.623 Γ— 10⁹⁸(99-digit number)
36231019146719892143…78441362180404646199
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
3.623 Γ— 10⁹⁸(99-digit number)
36231019146719892143…78441362180404646199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.246 Γ— 10⁹⁸(99-digit number)
72462038293439784286…56882724360809292399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.449 Γ— 10⁹⁹(100-digit number)
14492407658687956857…13765448721618584799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.898 Γ— 10⁹⁹(100-digit number)
28984815317375913714…27530897443237169599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.796 Γ— 10⁹⁹(100-digit number)
57969630634751827429…55061794886474339199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.159 Γ— 10¹⁰⁰(101-digit number)
11593926126950365485…10123589772948678399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.318 Γ— 10¹⁰⁰(101-digit number)
23187852253900730971…20247179545897356799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.637 Γ— 10¹⁰⁰(101-digit number)
46375704507801461943…40494359091794713599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.275 Γ— 10¹⁰⁰(101-digit number)
92751409015602923887…80988718183589427199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.855 Γ— 10¹⁰¹(102-digit number)
18550281803120584777…61977436367178854399
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,707,526 XPMΒ·at block #6,807,935 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