Block #960,265

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/3/2015, 7:55:27 PM · Difficulty 10.8869 · 5,832,691 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
115e1a5a73800d4e7c4b7b5fc57cf5ee72a44de0d8a163aad4d6a8ff0a19c9f2

Height

#960,265

Difficulty

10.886894

Transactions

3

Size

658 B

Version

2

Bits

0ae30b84

Nonce

1,459,451,202

Timestamp

3/3/2015, 7:55:27 PM

Confirmations

5,832,691

Merkle Root

44a2f840499a366519b39a8e5fdd0851375722e1bfffe81cb6e7e16d7d5238df
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.

3.184 × 10⁹⁵(96-digit number)
31846093280333167658…30178086062291467519
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
3.184 × 10⁹⁵(96-digit number)
31846093280333167658…30178086062291467519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.369 × 10⁹⁵(96-digit number)
63692186560666335316…60356172124582935039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.273 × 10⁹⁶(97-digit number)
12738437312133267063…20712344249165870079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.547 × 10⁹⁶(97-digit number)
25476874624266534126…41424688498331740159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.095 × 10⁹⁶(97-digit number)
50953749248533068253…82849376996663480319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.019 × 10⁹⁷(98-digit number)
10190749849706613650…65698753993326960639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.038 × 10⁹⁷(98-digit number)
20381499699413227301…31397507986653921279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.076 × 10⁹⁷(98-digit number)
40762999398826454602…62795015973307842559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.152 × 10⁹⁷(98-digit number)
81525998797652909205…25590031946615685119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.630 × 10⁹⁸(99-digit number)
16305199759530581841…51180063893231370239
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:57,587,634 XPM·at block #6,792,955 · updates every 60s
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