Block #87,488

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/28/2013, 10:31:21 PM · Difficulty 9.2759 · 6,708,319 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

581165458c0230471a2548c6c2483b425d679b0615516a287ca9681f14afd546

View on Chainz ↗

Height

#87,488

Difficulty

9.275885

Transactions

Size

207 B

Version

Bits

0946a06c

Nonce

245,295

Timestamp

7/28/2013, 10:31:21 PM

Confirmations

6,708,319

Mined by

⛏️ P2SHATe7tG7XMJeCcfKBVw1awGupC6yczDSDEp

Merkle Root

5600c5340c7c0f3fc866364359e935df9ee1564d687c5ec5bc8fb2cf960d0ebb

Transactions (1)

Coinbase5600c5340c7c0f…8fb2cf960d0ebb

1 in → 1 out11.6100 XPM109 B

ATe7tG7X…yczDSDEp

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.

1.234 × 10¹¹³(114-digit number)

12343989645102016663…33884277120840932759

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

1.234 × 10¹¹³(114-digit number)

12343989645102016663…33884277120840932759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.468 × 10¹¹³(114-digit number)

24687979290204033327…67768554241681865519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.937 × 10¹¹³(114-digit number)

49375958580408066654…35537108483363731039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.875 × 10¹¹³(114-digit number)

98751917160816133309…71074216966727462079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.975 × 10¹¹⁴(115-digit number)

19750383432163226661…42148433933454924159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.950 × 10¹¹⁴(115-digit number)

39500766864326453323…84296867866909848319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.900 × 10¹¹⁴(115-digit number)

79001533728652906647…68593735733819696639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.580 × 10¹¹⁵(116-digit number)

15800306745730581329…37187471467639393279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.160 × 10¹¹⁵(116-digit number)

31600613491461162659…74374942935278786559

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 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

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 1CC formula:

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

Cross-reference on Chainz Explorer