XPM Prime Explorer symbol
XPMPrime Explorer

Block #630,808

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2014, 5:04:18 AM Β· Difficulty 10.9616 Β· 6,187,062 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
99fa827b88236431da83b5a3470bee3babe8b2253efba15227a2ec02c665f342
View on Chainz β†—

Height

#630,808

Difficulty

10.961583

Transactions

2

Size

432 B

Version

2

Bits

0af62a52

Nonce

392,569,568

Timestamp

7/13/2014, 5:04:18 AM

Confirmations

6,187,062

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5f6d5914872ec1ff183a4c289edbc8ba5b8f7de526795f9a6a91589b3c7de886
Transactions (2)
Coinbase9fc09b0a49db18…b67b062bb1dfaa
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
0d1db1356a5e69…e3f8b695091066
1 in β†’ 2 out6.9416 XPM226 B
ARpjHv1k…4F9NvuWNARjWAxUJ…CXbfRB9Z
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.

7.021 Γ— 10⁹⁡(96-digit number)
70213813513876425925…55752740444682404479
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
7.021 Γ— 10⁹⁡(96-digit number)
70213813513876425925…55752740444682404479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.404 Γ— 10⁹⁢(97-digit number)
14042762702775285185…11505480889364808959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.808 Γ— 10⁹⁢(97-digit number)
28085525405550570370…23010961778729617919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.617 Γ— 10⁹⁢(97-digit number)
56171050811101140740…46021923557459235839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.123 Γ— 10⁹⁷(98-digit number)
11234210162220228148…92043847114918471679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.246 Γ— 10⁹⁷(98-digit number)
22468420324440456296…84087694229836943359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.493 Γ— 10⁹⁷(98-digit number)
44936840648880912592…68175388459673886719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.987 Γ— 10⁹⁷(98-digit number)
89873681297761825184…36350776919347773439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.797 Γ— 10⁹⁸(99-digit number)
17974736259552365036…72701553838695546879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.594 Γ— 10⁹⁸(99-digit number)
35949472519104730073…45403107677391093759
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:57,787,028 XPMΒ·at block #6,817,869 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