Block #87,090

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/28/2013, 3:22:07 PM · Difficulty 9.2803 · 6,707,618 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

09c18ab45bd9015549b358a8d79ef2cdb26ae5a50001da9f88a2670b575ad898

View on Chainz ↗

Height

#87,090

Difficulty

9.280266

Transactions

Size

475 B

Version

Bits

0947bf83

Nonce

59,893

Timestamp

7/28/2013, 3:22:07 PM

Confirmations

6,707,618

Mined by

⛏️ P2SHAdhmaJ1p1gqeX3dfcHueRxnjGJMhFRDjQ7

Merkle Root

e1ce6e951a05c3bd96c2114dd63e11dae12aa29df62c8f1c8e7493dc3068a1e7

Transactions (2)

Coinbase2bea355d33775b…de24fb10bcc38c

1 in → 1 out11.6000 XPM109 B

AdhmaJ1p…MhFRDjQ7

d79550f1ddb131…dcba977738a04d

2 in → 1 out23.2300 XPM271 B

AYKekaiF…jZyRVoKZ

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.

2.589 × 10¹⁰⁷(108-digit number)

25893030169346141589…39814025992625584439

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

2.589 × 10¹⁰⁷(108-digit number)

25893030169346141589…39814025992625584439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.178 × 10¹⁰⁷(108-digit number)

51786060338692283179…79628051985251168879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.035 × 10¹⁰⁸(109-digit number)

10357212067738456635…59256103970502337759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.071 × 10¹⁰⁸(109-digit number)

20714424135476913271…18512207941004675519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.142 × 10¹⁰⁸(109-digit number)

41428848270953826543…37024415882009351039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.285 × 10¹⁰⁸(109-digit number)

82857696541907653087…74048831764018702079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.657 × 10¹⁰⁹(110-digit number)

16571539308381530617…48097663528037404159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.314 × 10¹⁰⁹(110-digit number)

33143078616763061235…96195327056074808319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.628 × 10¹⁰⁹(110-digit number)

66286157233526122470…92390654112149616639

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