XPM Prime Explorer symbol
XPMPrime Explorer

Block #3,028,988

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/28/2019, 11:11:18 AM Β· Difficulty 11.1435 Β· 3,815,828 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
325f18f4fa7ff89bbd5a22dd78f7a330b3f191cadeae1ee4bb7335b121a6b3c5
View on Chainz β†—

Height

#3,028,988

Difficulty

11.143461

Transactions

2

Size

1.29 KB

Version

2

Bits

0b24b9e0

Nonce

1,445,827,778

Timestamp

1/28/2019, 11:11:18 AM

Confirmations

3,815,828

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

de96c1405e4861e1548a2e05e32a10dea650b389d4c5f8910b129af5c66ed312
Transactions (2)
Coinbase65a7cfda836845…666430069ef682
1 in β†’ 1 out8.0600 XPM110 B
AbXwmGxD…4XXYP765
63a5d941308761…05c4c183d3511d
7 in β†’ 2 out1302.5886 XPM1.09 KB
ASVrkg2Y…YAan5JmAAJor5KA8…3LSjzSo7
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.

1.307 Γ— 10⁹⁷(98-digit number)
13076910922898839162…20704017296565986559
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
1.307 Γ— 10⁹⁷(98-digit number)
13076910922898839162…20704017296565986559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.615 Γ— 10⁹⁷(98-digit number)
26153821845797678324…41408034593131973119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.230 Γ— 10⁹⁷(98-digit number)
52307643691595356649…82816069186263946239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.046 Γ— 10⁹⁸(99-digit number)
10461528738319071329…65632138372527892479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.092 Γ— 10⁹⁸(99-digit number)
20923057476638142659…31264276745055784959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.184 Γ— 10⁹⁸(99-digit number)
41846114953276285319…62528553490111569919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.369 Γ— 10⁹⁸(99-digit number)
83692229906552570639…25057106980223139839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.673 Γ— 10⁹⁹(100-digit number)
16738445981310514127…50114213960446279679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.347 Γ— 10⁹⁹(100-digit number)
33476891962621028255…00228427920892559359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.695 Γ— 10⁹⁹(100-digit number)
66953783925242056511…00456855841785118719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.339 Γ— 10¹⁰⁰(101-digit number)
13390756785048411302…00913711683570237439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:58,002,935 XPMΒ·at block #6,844,815 Β· updates every 60s
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