Block #2,473,903

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 1/15/2018, 8:22:32 AM · Difficulty 10.9633 · 4,366,639 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
04bdff26cf0a3325eab05673d61578e4e03f63af85b083c06dc6614b170449d1

Height

#2,473,903

Difficulty

10.963278

Transactions

3

Size

913 B

Version

2

Bits

0af69966

Nonce

64,848,956

Timestamp

1/15/2018, 8:22:32 AM

Confirmations

4,366,639

Merkle Root

40aae83d14176678a2399670ebd19c641f4324d1afd70d77b6f826b9c8f0f35b
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.

7.683 × 10⁹⁴(95-digit number)
76837950348641207626…64576730831900067839
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
7.683 × 10⁹⁴(95-digit number)
76837950348641207626…64576730831900067839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.536 × 10⁹⁵(96-digit number)
15367590069728241525…29153461663800135679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.073 × 10⁹⁵(96-digit number)
30735180139456483050…58306923327600271359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.147 × 10⁹⁵(96-digit number)
61470360278912966101…16613846655200542719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.229 × 10⁹⁶(97-digit number)
12294072055782593220…33227693310401085439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.458 × 10⁹⁶(97-digit number)
24588144111565186440…66455386620802170879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.917 × 10⁹⁶(97-digit number)
49176288223130372880…32910773241604341759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.835 × 10⁹⁶(97-digit number)
98352576446260745761…65821546483208683519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.967 × 10⁹⁷(98-digit number)
19670515289252149152…31643092966417367039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.934 × 10⁹⁷(98-digit number)
39341030578504298304…63286185932834734079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
7.868 × 10⁹⁷(98-digit number)
78682061157008596609…26572371865669468159
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:57,968,668 XPM·at block #6,840,541 · updates every 60s
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