XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,052,326

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/9/2015, 7:16:43 PM Β· Difficulty 10.7345 Β· 5,756,016 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c62676e36ed2290751353c2d6652523600a273696f776b055099f97b11f93ff9
View on Chainz β†—

Height

#1,052,326

Difficulty

10.734471

Transactions

2

Size

93.62 KB

Version

2

Bits

0abc0648

Nonce

2,265,161,937

Timestamp

5/9/2015, 7:16:43 PM

Confirmations

5,756,016

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

86949bc7205555eeed36b2c83ee3ec0163bcc7a6399e132f0c8c73a9c6d14c94
Transactions (2)
Coinbase03cdbf5e43f6cc…3cc3afbbb03473
1 in β†’ 1 out9.6200 XPM116 B
ANSXnLY2…Sd25TjkD
4a8977fb35d733…9ed11f92a074ba
838 in β†’ 1 out7256.8101 XPM93.42 KB
ATscm46d…49uwaxTP
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.

4.252 Γ— 10⁹⁢(97-digit number)
42520557374191157699…88468542638505401439
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
4.252 Γ— 10⁹⁢(97-digit number)
42520557374191157699…88468542638505401439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.504 Γ— 10⁹⁢(97-digit number)
85041114748382315398…76937085277010802879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.700 Γ— 10⁹⁷(98-digit number)
17008222949676463079…53874170554021605759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.401 Γ— 10⁹⁷(98-digit number)
34016445899352926159…07748341108043211519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.803 Γ— 10⁹⁷(98-digit number)
68032891798705852318…15496682216086423039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.360 Γ— 10⁹⁸(99-digit number)
13606578359741170463…30993364432172846079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.721 Γ— 10⁹⁸(99-digit number)
27213156719482340927…61986728864345692159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.442 Γ— 10⁹⁸(99-digit number)
54426313438964681855…23973457728691384319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.088 Γ— 10⁹⁹(100-digit number)
10885262687792936371…47946915457382768639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.177 Γ— 10⁹⁹(100-digit number)
21770525375585872742…95893830914765537279
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:57,710,793 XPMΒ·at block #6,808,341 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