Block #371,281

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/22/2014, 6:05:30 PM · Difficulty 10.4354 · 6,435,678 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5e103730a48b554d0d65169dfbcb5a74f5e26f7fb9c8d7e7a2105186f6e9432c

Height

#371,281

Difficulty

10.435447

Transactions

1

Size

1005 B

Version

2

Bits

0a6f7973

Nonce

60,482

Timestamp

1/22/2014, 6:05:30 PM

Confirmations

6,435,678

Merkle Root

7f5c9e793c0f4522f917d2a149509b1f52f72c7e2b8410c00cfcb3bf1b12f321
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.

1.800 × 10⁹⁹(100-digit number)
18005893081324061959…46349236402561254401
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
1.800 × 10⁹⁹(100-digit number)
18005893081324061959…46349236402561254401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.601 × 10⁹⁹(100-digit number)
36011786162648123918…92698472805122508801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.202 × 10⁹⁹(100-digit number)
72023572325296247836…85396945610245017601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.440 × 10¹⁰⁰(101-digit number)
14404714465059249567…70793891220490035201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.880 × 10¹⁰⁰(101-digit number)
28809428930118499134…41587782440980070401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.761 × 10¹⁰⁰(101-digit number)
57618857860236998268…83175564881960140801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.152 × 10¹⁰¹(102-digit number)
11523771572047399653…66351129763920281601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.304 × 10¹⁰¹(102-digit number)
23047543144094799307…32702259527840563201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.609 × 10¹⁰¹(102-digit number)
46095086288189598615…65404519055681126401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.219 × 10¹⁰¹(102-digit number)
92190172576379197230…30809038111362252801
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:57,699,770 XPM·at block #6,806,958 · updates every 60s
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