Block #1,041,911

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/2/2015, 5:14:59 PM · Difficulty 10.7227 · 5,753,632 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
26d7b4250aa2eff47ef11c0bd4ae9e5152e16a4f6ccf1e735f828eddaf7a95d9

Height

#1,041,911

Difficulty

10.722674

Transactions

2

Size

579 B

Version

2

Bits

0ab90123

Nonce

16,718,695

Timestamp

5/2/2015, 5:14:59 PM

Confirmations

5,753,632

Merkle Root

102d718e25b32d5de6798e041ef2adfba199c52c41aa6af3e898dfdf9467fb28
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.

2.957 × 10⁹⁵(96-digit number)
29574629937387097201…88039566057325194879
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
2.957 × 10⁹⁵(96-digit number)
29574629937387097201…88039566057325194879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.914 × 10⁹⁵(96-digit number)
59149259874774194402…76079132114650389759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.182 × 10⁹⁶(97-digit number)
11829851974954838880…52158264229300779519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.365 × 10⁹⁶(97-digit number)
23659703949909677760…04316528458601559039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.731 × 10⁹⁶(97-digit number)
47319407899819355521…08633056917203118079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
9.463 × 10⁹⁶(97-digit number)
94638815799638711043…17266113834406236159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.892 × 10⁹⁷(98-digit number)
18927763159927742208…34532227668812472319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.785 × 10⁹⁷(98-digit number)
37855526319855484417…69064455337624944639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.571 × 10⁹⁷(98-digit number)
75711052639710968834…38128910675249889279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.514 × 10⁹⁸(99-digit number)
15142210527942193766…76257821350499778559
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:57,608,407 XPM·at block #6,795,542 · updates every 60s
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