Block #2,271,394

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 8/28/2017, 5:30:29 AM · Difficulty 10.9536 · 4,565,073 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a0aa9f79a7c10a1dfbc399cbb0b620231a455dfb4c5768969f40044fadc6ea85

Height

#2,271,394

Difficulty

10.953633

Transactions

5

Size

2.09 KB

Version

2

Bits

0af4214e

Nonce

165,009,978

Timestamp

8/28/2017, 5:30:29 AM

Confirmations

4,565,073

Merkle Root

655bb20495953800c9d077bdee168decac88e6cccc6c4a0a0b409406073a4261
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.

3.302 × 10⁹⁵(96-digit number)
33022858452910392280…64547824133688354879
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
3.302 × 10⁹⁵(96-digit number)
33022858452910392280…64547824133688354879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.604 × 10⁹⁵(96-digit number)
66045716905820784561…29095648267376709759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.320 × 10⁹⁶(97-digit number)
13209143381164156912…58191296534753419519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.641 × 10⁹⁶(97-digit number)
26418286762328313824…16382593069506839039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.283 × 10⁹⁶(97-digit number)
52836573524656627649…32765186139013678079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.056 × 10⁹⁷(98-digit number)
10567314704931325529…65530372278027356159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.113 × 10⁹⁷(98-digit number)
21134629409862651059…31060744556054712319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.226 × 10⁹⁷(98-digit number)
42269258819725302119…62121489112109424639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.453 × 10⁹⁷(98-digit number)
84538517639450604238…24242978224218849279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.690 × 10⁹⁸(99-digit number)
16907703527890120847…48485956448437698559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
3.381 × 10⁹⁸(99-digit number)
33815407055780241695…96971912896875397119
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:57,936,008 XPM·at block #6,836,466 · updates every 60s
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