Block #375,537

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/25/2014, 7:02:28 PM · Difficulty 10.4237 · 6,438,763 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5d37da087a68083cc1b664e43687a4878dc0aee992aae126ff90ea7bdc613ecc

Height

#375,537

Difficulty

10.423712

Transactions

3

Size

915 B

Version

2

Bits

0a6c786a

Nonce

127,932

Timestamp

1/25/2014, 7:02:28 PM

Confirmations

6,438,763

Merkle Root

b5b22ce8cce4b280672e4c66cc2b0f3caf96bc699c3bfd5f293b10c4e8589a0d
Transactions (3)
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.

9.424 × 10¹⁰⁰(101-digit number)
94247983422180298789…58167738211670965839
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
9.424 × 10¹⁰⁰(101-digit number)
94247983422180298789…58167738211670965839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.884 × 10¹⁰¹(102-digit number)
18849596684436059757…16335476423341931679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.769 × 10¹⁰¹(102-digit number)
37699193368872119515…32670952846683863359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.539 × 10¹⁰¹(102-digit number)
75398386737744239031…65341905693367726719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.507 × 10¹⁰²(103-digit number)
15079677347548847806…30683811386735453439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.015 × 10¹⁰²(103-digit number)
30159354695097695612…61367622773470906879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.031 × 10¹⁰²(103-digit number)
60318709390195391225…22735245546941813759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.206 × 10¹⁰³(104-digit number)
12063741878039078245…45470491093883627519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.412 × 10¹⁰³(104-digit number)
24127483756078156490…90940982187767255039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.825 × 10¹⁰³(104-digit number)
48254967512156312980…81881964375534510079
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:57,758,464 XPM·at block #6,814,299 · updates every 60s
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