Block #2,632,950

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 4/28/2018, 4:08:55 AM · Difficulty 11.1767 · 4,204,470 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2e1fbad15674f99fd4ff550016473f6f90f46b197720182500fdf178dfed781f

Height

#2,632,950

Difficulty

11.176721

Transactions

2

Size

459 B

Version

2

Bits

0b2d3d93

Nonce

1,613,026,354

Timestamp

4/28/2018, 4:08:55 AM

Confirmations

4,204,470

Merkle Root

a9bc833b356a24e92ad441a45b8c92206de823f743dd6111173cf542563c2d5d
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.

1.026 × 10⁹⁴(95-digit number)
10263826479682609524…57249048156406667559
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
1.026 × 10⁹⁴(95-digit number)
10263826479682609524…57249048156406667559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.052 × 10⁹⁴(95-digit number)
20527652959365219048…14498096312813335119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.105 × 10⁹⁴(95-digit number)
41055305918730438096…28996192625626670239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.211 × 10⁹⁴(95-digit number)
82110611837460876192…57992385251253340479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.642 × 10⁹⁵(96-digit number)
16422122367492175238…15984770502506680959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.284 × 10⁹⁵(96-digit number)
32844244734984350476…31969541005013361919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.568 × 10⁹⁵(96-digit number)
65688489469968700953…63939082010026723839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.313 × 10⁹⁶(97-digit number)
13137697893993740190…27878164020053447679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.627 × 10⁹⁶(97-digit number)
26275395787987480381…55756328040106895359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.255 × 10⁹⁶(97-digit number)
52550791575974960762…11512656080213790719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.051 × 10⁹⁷(98-digit number)
10510158315194992152…23025312160427581439
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:57,943,680 XPM·at block #6,837,419 · updates every 60s
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