Block #52,591

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/16/2013, 11:10:00 AM · Difficulty 8.9139 · 6,755,489 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

4c5d0efc9da0266a26736c75f89477c4fa29c4ff0366bdf284230e890c84132d

View on Chainz ↗

Height

#52,591

Difficulty

8.913891

Transactions

Size

366 B

Version

Bits

08e9f4c9

Nonce

415

Timestamp

7/16/2013, 11:10:00 AM

Confirmations

6,755,489

Mined by

⛏️ P2SHAYrtgdMxKPSUprai4iVmQwiyphSnFDNzsA

Merkle Root

88f1a98dcafe38b30f21f8b9b0dbdf035a1bc8c7241417b4ce61a5a2373c1279

Transactions (2)

Coinbase76424ac9be9299…76afac053abb82

1 in → 1 out12.5800 XPM110 B

AYrtgdMx…SnFDNzsA

ce85667d73ef77…fd210792790a84

1 in → 1 out12.7000 XPM158 B

AW7xaLBs…KjHmcbd9

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.

6.449 × 10¹¹²(113-digit number)

64498127864052149242…96325870901854319251

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

6.449 × 10¹¹²(113-digit number)

64498127864052149242…96325870901854319251

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.289 × 10¹¹³(114-digit number)

12899625572810429848…92651741803708638501

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.579 × 10¹¹³(114-digit number)

25799251145620859697…85303483607417277001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.159 × 10¹¹³(114-digit number)

51598502291241719394…70606967214834554001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.031 × 10¹¹⁴(115-digit number)

10319700458248343878…41213934429669108001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.063 × 10¹¹⁴(115-digit number)

20639400916496687757…82427868859338216001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.127 × 10¹¹⁴(115-digit number)

41278801832993375515…64855737718676432001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.255 × 10¹¹⁴(115-digit number)

82557603665986751030…29711475437352864001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.651 × 10¹¹⁵(116-digit number)

16511520733197350206…59422950874705728001

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the Second 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer

Block #52,591

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