Block #1,111,992

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/17/2015, 3:41:21 AM · Difficulty 10.8909 · 5,698,777 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
49b4c786e2cf6ea71d26b388e693fea14b1696693f54a22d451af74c3853c516

Height

#1,111,992

Difficulty

10.890906

Transactions

2

Size

2.16 KB

Version

2

Bits

0ae41270

Nonce

258,563,777

Timestamp

6/17/2015, 3:41:21 AM

Confirmations

5,698,777

Merkle Root

01eff86692af3af157a8aa1a50a11d602f209ea05ff217fd0bf818e4c18ac7f4
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.

1.599 × 10⁹⁶(97-digit number)
15994644432615316363…55077403058239558399
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
1.599 × 10⁹⁶(97-digit number)
15994644432615316363…55077403058239558399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.198 × 10⁹⁶(97-digit number)
31989288865230632727…10154806116479116799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.397 × 10⁹⁶(97-digit number)
63978577730461265454…20309612232958233599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.279 × 10⁹⁷(98-digit number)
12795715546092253090…40619224465916467199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.559 × 10⁹⁷(98-digit number)
25591431092184506181…81238448931832934399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.118 × 10⁹⁷(98-digit number)
51182862184369012363…62476897863665868799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.023 × 10⁹⁸(99-digit number)
10236572436873802472…24953795727331737599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.047 × 10⁹⁸(99-digit number)
20473144873747604945…49907591454663475199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.094 × 10⁹⁸(99-digit number)
40946289747495209891…99815182909326950399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.189 × 10⁹⁸(99-digit number)
81892579494990419782…99630365818653900799
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:57,730,247 XPM·at block #6,810,768 · updates every 60s
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