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Block #2,703,372

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/13/2018, 7:30:57 AM Β· Difficulty 11.6291 Β· 4,133,142 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2b5a76b19781337398172700c16819fdc0926603e101ce83f70a2bd4eedece2c
View on Chainz β†—

Height

#2,703,372

Difficulty

11.629108

Transactions

2

Size

722 B

Version

2

Bits

0ba10d34

Nonce

195,858,378

Timestamp

6/13/2018, 7:30:57 AM

Confirmations

4,133,142

Mined by

⛏️ P2SHAcLjvF4PR2QBgEBsYnwcSdrDgaURF3AAUR

Merkle Root

f70d0f5ce0564e143d75b08dc3a6d3af31d8edef4e6214d14faf87fdd00f96f3
Transactions (2)
Coinbasec6a7a0ff660737…8237f37a4e9ee6
1 in β†’ 1 out7.3900 XPM110 B
AcLjvF4P…URF3AAUR
5176c2c257a35a…2d8c224773ed31
3 in β†’ 2 out500.0100 XPM522 B
Ab4pAke9…vMopsZneAQmjqzoU…5U6sbve9
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.

9.922 Γ— 10⁹⁴(95-digit number)
99225605704922790144…52654543594897412259
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
9.922 Γ— 10⁹⁴(95-digit number)
99225605704922790144…52654543594897412259
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.984 Γ— 10⁹⁡(96-digit number)
19845121140984558028…05309087189794824519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.969 Γ— 10⁹⁡(96-digit number)
39690242281969116057…10618174379589649039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.938 Γ— 10⁹⁡(96-digit number)
79380484563938232115…21236348759179298079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.587 Γ— 10⁹⁢(97-digit number)
15876096912787646423…42472697518358596159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.175 Γ— 10⁹⁢(97-digit number)
31752193825575292846…84945395036717192319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.350 Γ— 10⁹⁢(97-digit number)
63504387651150585692…69890790073434384639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.270 Γ— 10⁹⁷(98-digit number)
12700877530230117138…39781580146868769279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.540 Γ— 10⁹⁷(98-digit number)
25401755060460234276…79563160293737538559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.080 Γ— 10⁹⁷(98-digit number)
50803510120920468553…59126320587475077119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.016 Γ— 10⁹⁸(99-digit number)
10160702024184093710…18252641174950154239
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:57,936,388 XPMΒ·at block #6,836,513 Β· updates every 60s
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