Block #377,165

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/26/2014, 10:06:05 PM · Difficulty 10.4246 · 6,449,955 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
170b6f1bec88c7b3b1f88b6c768ef36a96dfce75266113d20850eecf4b36bc3c

Height

#377,165

Difficulty

10.424557

Transactions

4

Size

1.46 KB

Version

2

Bits

0a6cafc0

Nonce

91,096

Timestamp

1/26/2014, 10:06:05 PM

Confirmations

6,449,955

Merkle Root

47e6d3a3a21d602a97923d25c80bb4dc11d89375330adf2d78a9977291095c1b
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.

5.519 × 10⁹⁸(99-digit number)
55198626944234894985…85141662638670021019
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
5.519 × 10⁹⁸(99-digit number)
55198626944234894985…85141662638670021019
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.103 × 10⁹⁹(100-digit number)
11039725388846978997…70283325277340042039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.207 × 10⁹⁹(100-digit number)
22079450777693957994…40566650554680084079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.415 × 10⁹⁹(100-digit number)
44158901555387915988…81133301109360168159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
8.831 × 10⁹⁹(100-digit number)
88317803110775831976…62266602218720336319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.766 × 10¹⁰⁰(101-digit number)
17663560622155166395…24533204437440672639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.532 × 10¹⁰⁰(101-digit number)
35327121244310332790…49066408874881345279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.065 × 10¹⁰⁰(101-digit number)
70654242488620665581…98132817749762690559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.413 × 10¹⁰¹(102-digit number)
14130848497724133116…96265635499525381119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.826 × 10¹⁰¹(102-digit number)
28261696995448266232…92531270999050762239
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:57,861,141 XPM·at block #6,827,119 · updates every 60s
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