Block #373,980

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/24/2014, 4:28:34 PM · Difficulty 10.4276 · 6,416,961 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ec4c62978467b95a4ca826b3b73894757f33b50e0acca4a24b4d9cf2a466cbf6

Height

#373,980

Difficulty

10.427649

Transactions

3

Size

1.04 KB

Version

2

Bits

0a6d7a6b

Nonce

121,081

Timestamp

1/24/2014, 4:28:34 PM

Confirmations

6,416,961

Merkle Root

67202fd181246c8abc9f2ed25fa8d2b8760a315d254127cfb48bb31a6647d18e
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.

6.645 × 10⁹⁹(100-digit number)
66450934682354108420…09936707526006137439
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
6.645 × 10⁹⁹(100-digit number)
66450934682354108420…09936707526006137439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.329 × 10¹⁰⁰(101-digit number)
13290186936470821684…19873415052012274879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.658 × 10¹⁰⁰(101-digit number)
26580373872941643368…39746830104024549759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.316 × 10¹⁰⁰(101-digit number)
53160747745883286736…79493660208049099519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.063 × 10¹⁰¹(102-digit number)
10632149549176657347…58987320416098199039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.126 × 10¹⁰¹(102-digit number)
21264299098353314694…17974640832196398079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.252 × 10¹⁰¹(102-digit number)
42528598196706629389…35949281664392796159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
8.505 × 10¹⁰¹(102-digit number)
85057196393413258778…71898563328785592319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.701 × 10¹⁰²(103-digit number)
17011439278682651755…43797126657571184639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.402 × 10¹⁰²(103-digit number)
34022878557365303511…87594253315142369279
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:57,571,545 XPM·at block #6,790,940 · updates every 60s