Block #3,276,904

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 7/22/2019, 10:34:44 AM · Difficulty 10.9950 · 3,560,874 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fb87c1072afe28f53aab58595117c4e7fdaa22ef1ae6b9f605e678a4efa77a38

Height

#3,276,904

Difficulty

10.995032

Transactions

2

Size

1.14 KB

Version

2

Bits

0afeba66

Nonce

889,711,937

Timestamp

7/22/2019, 10:34:44 AM

Confirmations

3,560,874

Merkle Root

2ca8db74969808d41748c706cd9770e959cdcca649ec9ce794e06d6d58fe63c9
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.

3.736 × 10⁹⁶(97-digit number)
37365535280527762834…76205254469370588159
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
3.736 × 10⁹⁶(97-digit number)
37365535280527762834…76205254469370588159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.473 × 10⁹⁶(97-digit number)
74731070561055525669…52410508938741176319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.494 × 10⁹⁷(98-digit number)
14946214112211105133…04821017877482352639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.989 × 10⁹⁷(98-digit number)
29892428224422210267…09642035754964705279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.978 × 10⁹⁷(98-digit number)
59784856448844420535…19284071509929410559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.195 × 10⁹⁸(99-digit number)
11956971289768884107…38568143019858821119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.391 × 10⁹⁸(99-digit number)
23913942579537768214…77136286039717642239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.782 × 10⁹⁸(99-digit number)
47827885159075536428…54272572079435284479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.565 × 10⁹⁸(99-digit number)
95655770318151072856…08545144158870568959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.913 × 10⁹⁹(100-digit number)
19131154063630214571…17090288317741137919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
3.826 × 10⁹⁹(100-digit number)
38262308127260429142…34180576635482275839
Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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
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 × 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:57,946,560 XPM·at block #6,837,777 · updates every 60s
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