XPM Prime Explorer symbol
XPMPrime Explorer

Block #293,605

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/4/2013, 10:04:41 AM Β· Difficulty 9.9907 Β· 6,512,093 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
04308057a1381009951b23327d277dc4f9d46ae6f0cce28ccd6da841f06d8827
View on Chainz β†—

Height

#293,605

Difficulty

9.990695

Transactions

2

Size

426 B

Version

2

Bits

09fd9e35

Nonce

20,033

Timestamp

12/4/2013, 10:04:41 AM

Confirmations

6,512,093

Mined by

⛏️ P2SHARnDz4GE5QABqsPrhSffpzM4WTjgY1beXE

Merkle Root

c050e52aff4784a64996a748262078861d2a7e0e821d2f7ff539430d81f45a32
Transactions (2)
Coinbase59693f4da6ecf1…863834e5d003c1
1 in β†’ 1 out10.0100 XPM109 B
ARnDz4GE…jgY1beXE
80f0c33ab8a2b2…3c5dc29edcbd3d
1 in β†’ 2 out99.9900 XPM227 B
ALU4tFVK…GD9L8tKAAdqe4UX5…6QHTh165
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.

9.976 Γ— 10⁹³(94-digit number)
99769816573706757429…99524421173292341879
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
9.976 Γ— 10⁹³(94-digit number)
99769816573706757429…99524421173292341879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.995 Γ— 10⁹⁴(95-digit number)
19953963314741351485…99048842346584683759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.990 Γ— 10⁹⁴(95-digit number)
39907926629482702971…98097684693169367519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.981 Γ— 10⁹⁴(95-digit number)
79815853258965405943…96195369386338735039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.596 Γ— 10⁹⁡(96-digit number)
15963170651793081188…92390738772677470079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.192 Γ— 10⁹⁡(96-digit number)
31926341303586162377…84781477545354940159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.385 Γ— 10⁹⁡(96-digit number)
63852682607172324755…69562955090709880319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.277 Γ— 10⁹⁢(97-digit number)
12770536521434464951…39125910181419760639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.554 Γ— 10⁹⁢(97-digit number)
25541073042868929902…78251820362839521279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.108 Γ— 10⁹⁢(97-digit number)
51082146085737859804…56503640725679042559
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:57,689,665 XPMΒ·at block #6,805,697 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