Block #375,429

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/25/2014, 5:12:18 PM · Difficulty 10.4241 · 6,428,358 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
de016e5a4726840b94aa20512f8689a6ace695ca3199d6f760f38f37568ac7ef

Height

#375,429

Difficulty

10.424114

Transactions

2

Size

872 B

Version

2

Bits

0a6c92b7

Nonce

222,074

Timestamp

1/25/2014, 5:12:18 PM

Confirmations

6,428,358

Merkle Root

29ab03cbcf1dba60b9615c2cf419293ae5f043ce73a511d291f25c4d69088171
Transactions (2)
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.

8.210 × 10¹⁰⁰(101-digit number)
82100363777711388933…68679312787538164959
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
8.210 × 10¹⁰⁰(101-digit number)
82100363777711388933…68679312787538164959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.642 × 10¹⁰¹(102-digit number)
16420072755542277786…37358625575076329919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.284 × 10¹⁰¹(102-digit number)
32840145511084555573…74717251150152659839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.568 × 10¹⁰¹(102-digit number)
65680291022169111146…49434502300305319679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.313 × 10¹⁰²(103-digit number)
13136058204433822229…98869004600610639359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.627 × 10¹⁰²(103-digit number)
26272116408867644458…97738009201221278719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.254 × 10¹⁰²(103-digit number)
52544232817735288917…95476018402442557439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.050 × 10¹⁰³(104-digit number)
10508846563547057783…90952036804885114879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.101 × 10¹⁰³(104-digit number)
21017693127094115566…81904073609770229759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.203 × 10¹⁰³(104-digit number)
42035386254188231133…63808147219540459519
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,674,337 XPM·at block #6,803,786 · updates every 60s
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