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Block #2,623,282

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/21/2018, 6:36:35 AM Β· Difficulty 11.2192 Β· 4,213,291 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bd79c4e8bc334fb6f135efe87b40737a6aac1da90fbc6cd3eaf10a0ebd92e56c
View on Chainz β†—

Height

#2,623,282

Difficulty

11.219224

Transactions

2

Size

393 B

Version

2

Bits

0b381f10

Nonce

351,016,620

Timestamp

4/21/2018, 6:36:35 AM

Confirmations

4,213,291

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

a83527bb0c777ae2238311e8a0e2a49ef2c02a5051422843ee8863a2208611e2
Transactions (2)
Coinbasefa7277d773f94f…5d73faeae80975
1 in β†’ 1 out7.9400 XPM110 B
Adqah8zh…1WwoHJ9t
7a230701f91dad…0165fdf164f9c9
1 in β†’ 1 out550.0000 XPM192 B
AGGn6SJu…QVxKbSrU
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.

5.780 Γ— 10⁹⁢(97-digit number)
57803875145483124406…52331327915814604799
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
5.780 Γ— 10⁹⁢(97-digit number)
57803875145483124406…52331327915814604799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.156 Γ— 10⁹⁷(98-digit number)
11560775029096624881…04662655831629209599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.312 Γ— 10⁹⁷(98-digit number)
23121550058193249762…09325311663258419199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.624 Γ— 10⁹⁷(98-digit number)
46243100116386499524…18650623326516838399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.248 Γ— 10⁹⁷(98-digit number)
92486200232772999049…37301246653033676799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.849 Γ— 10⁹⁸(99-digit number)
18497240046554599809…74602493306067353599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.699 Γ— 10⁹⁸(99-digit number)
36994480093109199619…49204986612134707199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.398 Γ— 10⁹⁸(99-digit number)
73988960186218399239…98409973224269414399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.479 Γ— 10⁹⁹(100-digit number)
14797792037243679847…96819946448538828799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.959 Γ— 10⁹⁹(100-digit number)
29595584074487359695…93639892897077657599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.919 Γ— 10⁹⁹(100-digit number)
59191168148974719391…87279785794155315199
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:57,936,849 XPMΒ·at block #6,836,572 Β· updates every 60s
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