Block #1,471,388

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/25/2016, 10:57:08 AM · Difficulty 10.7107 · 5,341,596 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
95479ffbb3f4020e8a9986907545e4f6375f82d9f8ccbe0e531350a0db1dd866

Height

#1,471,388

Difficulty

10.710653

Transactions

2

Size

1.14 KB

Version

2

Bits

0ab5ed57

Nonce

1,484,177,451

Timestamp

2/25/2016, 10:57:08 AM

Confirmations

5,341,596

Merkle Root

1caa97713fb8e19041b655f378b11ec5ac1fe7c35aa23128ebfc20d74816145a
Transactions (2)
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.181 × 10⁹⁵(96-digit number)
11815876965339215365…71105368638705994239
Discovered Prime Numbers
p_k = 2^k × origin − 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 − 1
1.181 × 10⁹⁵(96-digit number)
11815876965339215365…71105368638705994239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.363 × 10⁹⁵(96-digit number)
23631753930678430730…42210737277411988479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.726 × 10⁹⁵(96-digit number)
47263507861356861461…84421474554823976959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.452 × 10⁹⁵(96-digit number)
94527015722713722922…68842949109647953919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.890 × 10⁹⁶(97-digit number)
18905403144542744584…37685898219295907839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.781 × 10⁹⁶(97-digit number)
37810806289085489169…75371796438591815679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.562 × 10⁹⁶(97-digit number)
75621612578170978338…50743592877183631359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.512 × 10⁹⁷(98-digit number)
15124322515634195667…01487185754367262719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.024 × 10⁹⁷(98-digit number)
30248645031268391335…02974371508734525439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.049 × 10⁹⁷(98-digit number)
60497290062536782670…05948743017469050879
Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆
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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,747,909 XPM·at block #6,812,983 · updates every 60s
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