Block #361,970

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/16/2014, 10:05:25 AM · Difficulty 10.4109 · 6,454,472 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0b42626a37d92759b7d00e7b45c7b0610559cdab6decf1b558b573138a400e3e

Height

#361,970

Difficulty

10.410865

Transactions

4

Size

1.49 KB

Version

2

Bits

0a692e74

Nonce

2,581

Timestamp

1/16/2014, 10:05:25 AM

Confirmations

6,454,472

Merkle Root

5f9d11d2391d934f7ceedb9766bd1ef91100b08f231b5977e7428cdd797e9ea1
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.

7.820 × 10¹⁰²(103-digit number)
78201611121341323875…39215608953599436801
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
7.820 × 10¹⁰²(103-digit number)
78201611121341323875…39215608953599436801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.564 × 10¹⁰³(104-digit number)
15640322224268264775…78431217907198873601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.128 × 10¹⁰³(104-digit number)
31280644448536529550…56862435814397747201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.256 × 10¹⁰³(104-digit number)
62561288897073059100…13724871628795494401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.251 × 10¹⁰⁴(105-digit number)
12512257779414611820…27449743257590988801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.502 × 10¹⁰⁴(105-digit number)
25024515558829223640…54899486515181977601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.004 × 10¹⁰⁴(105-digit number)
50049031117658447280…09798973030363955201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.000 × 10¹⁰⁵(106-digit number)
10009806223531689456…19597946060727910401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.001 × 10¹⁰⁵(106-digit number)
20019612447063378912…39195892121455820801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.003 × 10¹⁰⁵(106-digit number)
40039224894126757824…78391784242911641601
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:57,775,662 XPM·at block #6,816,441 · updates every 60s
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