Block #364,445

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/18/2014, 2:04:09 AM · Difficulty 10.4213 · 6,466,035 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fa5dca1b8d55a1c79831b2251d00392de6b856ba2dcb9145735aae5379489ccf

Height

#364,445

Difficulty

10.421280

Transactions

4

Size

881 B

Version

2

Bits

0a6bd905

Nonce

996,199

Timestamp

1/18/2014, 2:04:09 AM

Confirmations

6,466,035

Merkle Root

c5c6385ad732c40e0f3a26cfe0f73569fa19cbf022d82283a82f57a47353e240
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.

5.758 × 10⁹⁸(99-digit number)
57582289969452127746…59521566400376920321
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
5.758 × 10⁹⁸(99-digit number)
57582289969452127746…59521566400376920321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.151 × 10⁹⁹(100-digit number)
11516457993890425549…19043132800753840641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.303 × 10⁹⁹(100-digit number)
23032915987780851098…38086265601507681281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.606 × 10⁹⁹(100-digit number)
46065831975561702196…76172531203015362561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.213 × 10⁹⁹(100-digit number)
92131663951123404393…52345062406030725121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.842 × 10¹⁰⁰(101-digit number)
18426332790224680878…04690124812061450241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.685 × 10¹⁰⁰(101-digit number)
36852665580449361757…09380249624122900481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.370 × 10¹⁰⁰(101-digit number)
73705331160898723514…18760499248245800961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.474 × 10¹⁰¹(102-digit number)
14741066232179744702…37520998496491601921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.948 × 10¹⁰¹(102-digit number)
29482132464359489405…75041996992983203841
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:57,888,088 XPM·at block #6,830,479 · updates every 60s
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