Block #477,426

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/6/2014, 11:13:25 AM · Difficulty 10.4816 · 6,332,797 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ea4c3758ffa11430a0638396593e5755b652482e88e43e04260d4bde6fdb3f33

Height

#477,426

Difficulty

10.481617

Transactions

2

Size

730 B

Version

2

Bits

0a7b4b3c

Nonce

482,802

Timestamp

4/6/2014, 11:13:25 AM

Confirmations

6,332,797

Merkle Root

68fc1f27c4bcfc96a75bf033622b3f4b408e572169dbc90aa6de6a2b722b33c6
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.

4.148 × 10¹⁰⁴(105-digit number)
41484008194978051195…16440737005238507519
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
4.148 × 10¹⁰⁴(105-digit number)
41484008194978051195…16440737005238507519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.296 × 10¹⁰⁴(105-digit number)
82968016389956102390…32881474010477015039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.659 × 10¹⁰⁵(106-digit number)
16593603277991220478…65762948020954030079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.318 × 10¹⁰⁵(106-digit number)
33187206555982440956…31525896041908060159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.637 × 10¹⁰⁵(106-digit number)
66374413111964881912…63051792083816120319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.327 × 10¹⁰⁶(107-digit number)
13274882622392976382…26103584167632240639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.654 × 10¹⁰⁶(107-digit number)
26549765244785952764…52207168335264481279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.309 × 10¹⁰⁶(107-digit number)
53099530489571905529…04414336670528962559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.061 × 10¹⁰⁷(108-digit number)
10619906097914381105…08828673341057925119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.123 × 10¹⁰⁷(108-digit number)
21239812195828762211…17657346682115850239
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:57,725,860 XPM·at block #6,810,222 · updates every 60s
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