Block #377,385

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/27/2014, 2:13:35 AM · Difficulty 10.4218 · 6,453,109 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
31d78da6c01811486804f8a88bc00eabcb69cd4ed0c24ec8e54b1ddb96c9bc85

Height

#377,385

Difficulty

10.421840

Transactions

1

Size

800 B

Version

2

Bits

0a6bfdb8

Nonce

98,240

Timestamp

1/27/2014, 2:13:35 AM

Confirmations

6,453,109

Merkle Root

c19ff8a09b587d999d05aa3198fd30c50157257f9fbae65b322dfc66d4abfbd8
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.

7.556 × 10⁹⁷(98-digit number)
75569207587320700700…59764796671650344961
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
7.556 × 10⁹⁷(98-digit number)
75569207587320700700…59764796671650344961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.511 × 10⁹⁸(99-digit number)
15113841517464140140…19529593343300689921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.022 × 10⁹⁸(99-digit number)
30227683034928280280…39059186686601379841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.045 × 10⁹⁸(99-digit number)
60455366069856560560…78118373373202759681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.209 × 10⁹⁹(100-digit number)
12091073213971312112…56236746746405519361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.418 × 10⁹⁹(100-digit number)
24182146427942624224…12473493492811038721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.836 × 10⁹⁹(100-digit number)
48364292855885248448…24946986985622077441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.672 × 10⁹⁹(100-digit number)
96728585711770496896…49893973971244154881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.934 × 10¹⁰⁰(101-digit number)
19345717142354099379…99787947942488309761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.869 × 10¹⁰⁰(101-digit number)
38691434284708198758…99575895884976619521
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:57,888,202 XPM·at block #6,830,493 · updates every 60s
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