Block #370,172

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/21/2014, 9:54:15 PM · Difficulty 10.4476 · 6,439,304 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5c8cd7b78a1fdf9a0acfdf1e56c945f2d49fa2e59d16150d847415cd99a8e5d4

Height

#370,172

Difficulty

10.447552

Transactions

1

Size

229 B

Version

2

Bits

0a7292cb

Nonce

168,526

Timestamp

1/21/2014, 9:54:15 PM

Confirmations

6,439,304

Merkle Root

e9ddddbcb9dae61a669c61cabcf1fb23aeba3d8510661ee55402dd771297a4e2
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.

9.372 × 10¹⁰⁰(101-digit number)
93727121637033284911…74764083347362856191
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
9.372 × 10¹⁰⁰(101-digit number)
93727121637033284911…74764083347362856191
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.874 × 10¹⁰¹(102-digit number)
18745424327406656982…49528166694725712381
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.749 × 10¹⁰¹(102-digit number)
37490848654813313964…99056333389451424761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.498 × 10¹⁰¹(102-digit number)
74981697309626627929…98112666778902849521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.499 × 10¹⁰²(103-digit number)
14996339461925325585…96225333557805699041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.999 × 10¹⁰²(103-digit number)
29992678923850651171…92450667115611398081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.998 × 10¹⁰²(103-digit number)
59985357847701302343…84901334231222796161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.199 × 10¹⁰³(104-digit number)
11997071569540260468…69802668462445592321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.399 × 10¹⁰³(104-digit number)
23994143139080520937…39605336924891184641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.798 × 10¹⁰³(104-digit number)
47988286278161041874…79210673849782369281
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:57,719,880 XPM·at block #6,809,475 · updates every 60s
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