Block #377,571

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/27/2014, 5:37:04 AM · Difficulty 10.4194 · 6,417,962 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cfa6e5a86d5b608c92e162e6039a9b4634864a543939fcc0387cb54694824d2c

Height

#377,571

Difficulty

10.419442

Transactions

2

Size

878 B

Version

2

Bits

0a6b6088

Nonce

42,876

Timestamp

1/27/2014, 5:37:04 AM

Confirmations

6,417,962

Merkle Root

5056be0a490855e37bc12a18d1ec0a8680996f481feb070bd7415fc89f11bff6
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.

3.738 × 10⁹⁹(100-digit number)
37382254241060106637…69223118078622552599
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
3.738 × 10⁹⁹(100-digit number)
37382254241060106637…69223118078622552599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.476 × 10⁹⁹(100-digit number)
74764508482120213274…38446236157245105199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.495 × 10¹⁰⁰(101-digit number)
14952901696424042654…76892472314490210399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.990 × 10¹⁰⁰(101-digit number)
29905803392848085309…53784944628980420799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.981 × 10¹⁰⁰(101-digit number)
59811606785696170619…07569889257960841599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.196 × 10¹⁰¹(102-digit number)
11962321357139234123…15139778515921683199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.392 × 10¹⁰¹(102-digit number)
23924642714278468247…30279557031843366399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.784 × 10¹⁰¹(102-digit number)
47849285428556936495…60559114063686732799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.569 × 10¹⁰¹(102-digit number)
95698570857113872991…21118228127373465599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.913 × 10¹⁰²(103-digit number)
19139714171422774598…42236456254746931199
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:57,608,327 XPM·at block #6,795,532 · updates every 60s
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