Block #477,626

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/6/2014, 1:50:19 PM · Difficulty 10.4860 · 6,324,611 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

bbda3ca407708f823d88beba104b96c1a425d029ab48646754d407ed3a7aaf81

View on Chainz ↗

Height

#477,626

Difficulty

10.486016

Transactions

Size

903 B

Version

Bits

0a7c6b85

Nonce

167,931

Timestamp

4/6/2014, 1:50:19 PM

Confirmations

6,324,611

Mined by

⛏️ IaSAAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

6db6ad8df53e6511c8bca1404cd4aaecfa049a9b859630bd434d009879a88a96

Transactions (1)

Coinbase6db6ad8df53e65…4d009879a88a96

1 in → 22 out9.0789 XPM810 B

AQvZBsUo…hppgRZTJ AQ8QAT3J…rCFKuVbR AWMrD5hP…ZwsoxvZ3 ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn

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.

1.710 × 10¹⁰²(103-digit number)

17104829703203968914…17460138549689057279

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.

origin − 1

1.710 × 10¹⁰²(103-digit number)

17104829703203968914…17460138549689057279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.420 × 10¹⁰²(103-digit number)

34209659406407937828…34920277099378114559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.841 × 10¹⁰²(103-digit number)

68419318812815875657…69840554198756229119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.368 × 10¹⁰³(104-digit number)

13683863762563175131…39681108397512458239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.736 × 10¹⁰³(104-digit number)

27367727525126350262…79362216795024916479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.473 × 10¹⁰³(104-digit number)

54735455050252700525…58724433590049832959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.094 × 10¹⁰⁴(105-digit number)

10947091010050540105…17448867180099665919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.189 × 10¹⁰⁴(105-digit number)

21894182020101080210…34897734360199331839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.378 × 10¹⁰⁴(105-digit number)

43788364040202160420…69795468720398663679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.757 × 10¹⁰⁴(105-digit number)

87576728080404320841…39590937440797327359

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, …

Cross-reference on Chainz Explorer