Block #1,085,101

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/1/2015, 5:33:42 AM · Difficulty 10.7596 · 5,720,760 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
68fbc5c740bb709f24eea52733d3a258d2b6d3d4785683c56298c95fcd0637e4

Height

#1,085,101

Difficulty

10.759610

Transactions

1

Size

242 B

Version

2

Bits

0ac275c5

Nonce

1,910,448,913

Timestamp

6/1/2015, 5:33:42 AM

Confirmations

5,720,760

Merkle Root

a1c3a70117da96efaedf6763e31607e4c7175b6009ba001726ebe2762eae50a5
Transactions (1)
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.

1.953 × 10⁹⁵(96-digit number)
19530636595415304788…83740390430770791361
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
1.953 × 10⁹⁵(96-digit number)
19530636595415304788…83740390430770791361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.906 × 10⁹⁵(96-digit number)
39061273190830609577…67480780861541582721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.812 × 10⁹⁵(96-digit number)
78122546381661219154…34961561723083165441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.562 × 10⁹⁶(97-digit number)
15624509276332243830…69923123446166330881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.124 × 10⁹⁶(97-digit number)
31249018552664487661…39846246892332661761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.249 × 10⁹⁶(97-digit number)
62498037105328975323…79692493784665323521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.249 × 10⁹⁷(98-digit number)
12499607421065795064…59384987569330647041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.499 × 10⁹⁷(98-digit number)
24999214842131590129…18769975138661294081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.999 × 10⁹⁷(98-digit number)
49998429684263180259…37539950277322588161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.999 × 10⁹⁷(98-digit number)
99996859368526360518…75079900554645176321
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,690,970 XPM·at block #6,805,860 · updates every 60s
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