Block #1,485,187

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/5/2016, 8:07:42 PM · Difficulty 10.7272 · 5,359,371 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
85e9d75619c2d21333901f867ba9f863c5800d54d16b765eb3317fc189ffd787

Height

#1,485,187

Difficulty

10.727214

Transactions

2

Size

1.28 KB

Version

2

Bits

0aba2ab6

Nonce

236,452,056

Timestamp

3/5/2016, 8:07:42 PM

Confirmations

5,359,371

Merkle Root

e552c3053ca860f751dfc314aaf104d226fc13e93ce3736c7dfc62949426221d
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.

7.419 × 10⁹⁵(96-digit number)
74199662698867996397…42332839386988601601
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
7.419 × 10⁹⁵(96-digit number)
74199662698867996397…42332839386988601601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.483 × 10⁹⁶(97-digit number)
14839932539773599279…84665678773977203201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.967 × 10⁹⁶(97-digit number)
29679865079547198558…69331357547954406401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.935 × 10⁹⁶(97-digit number)
59359730159094397117…38662715095908812801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.187 × 10⁹⁷(98-digit number)
11871946031818879423…77325430191817625601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.374 × 10⁹⁷(98-digit number)
23743892063637758847…54650860383635251201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.748 × 10⁹⁷(98-digit number)
47487784127275517694…09301720767270502401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.497 × 10⁹⁷(98-digit number)
94975568254551035388…18603441534541004801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.899 × 10⁹⁸(99-digit number)
18995113650910207077…37206883069082009601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.799 × 10⁹⁸(99-digit number)
37990227301820414155…74413766138164019201
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:58,000,867 XPM·at block #6,844,557 · updates every 60s
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