Block #605,186

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/28/2014, 8:27:07 AM · Difficulty 10.9098 · 6,203,726 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c29c5718dd4218232f27def72e131970ddbd6476e5a5012c40a3d24faf4da7ea

Height

#605,186

Difficulty

10.909804

Transactions

4

Size

1.01 KB

Version

2

Bits

0ae8e8e5

Nonce

459,941,859

Timestamp

6/28/2014, 8:27:07 AM

Confirmations

6,203,726

Merkle Root

db90fa76dfcafefa4bef67c4c6f5894b47bf30f19934af840743f6297df33592
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.

4.750 × 10⁹⁷(98-digit number)
47505242556014439866…04085476373459842001
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
4.750 × 10⁹⁷(98-digit number)
47505242556014439866…04085476373459842001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.501 × 10⁹⁷(98-digit number)
95010485112028879732…08170952746919684001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.900 × 10⁹⁸(99-digit number)
19002097022405775946…16341905493839368001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.800 × 10⁹⁸(99-digit number)
38004194044811551893…32683810987678736001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.600 × 10⁹⁸(99-digit number)
76008388089623103786…65367621975357472001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.520 × 10⁹⁹(100-digit number)
15201677617924620757…30735243950714944001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.040 × 10⁹⁹(100-digit number)
30403355235849241514…61470487901429888001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.080 × 10⁹⁹(100-digit number)
60806710471698483028…22940975802859776001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.216 × 10¹⁰⁰(101-digit number)
12161342094339696605…45881951605719552001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.432 × 10¹⁰⁰(101-digit number)
24322684188679393211…91763903211439104001
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:57,715,351 XPM·at block #6,808,911 · updates every 60s
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