Block #87,232

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/28/2013, 6:02:55 PM · Difficulty 9.2779 · 6,708,975 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

8b97803aea0e3a14be7ee3ca57aa38aa39f8f2400d5b001a17f55d7ba0c52348

View on Chainz ↗

Height

#87,232

Difficulty

9.277860

Transactions

Size

432 B

Version

Bits

094721d6

Nonce

161,770

Timestamp

7/28/2013, 6:02:55 PM

Confirmations

6,708,975

Mined by

⛏️ P2SHAHBeUT2xwpHmrLqUQCW3Pk71DwtfABaTAa

Merkle Root

2c796826fe2fb6014a1e99ab6653ca0992260b16616a2072255640e55d76770b

Transactions (2)

Coinbase542413e16252c0…c57be9b165fd6b

1 in → 1 out11.6100 XPM109 B

AHBeUT2x…tfABaTAa

0d091e39f7be55…de48905e3b3ce4

1 in → 2 out11.6000 XPM226 B

AKXG5vUo…7NyYyifR AUTFF94a…DNKSqTBU

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.

3.601 × 10¹¹⁰(111-digit number)

36018804828490989474…76028480418737964429

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

3.601 × 10¹¹⁰(111-digit number)

36018804828490989474…76028480418737964429

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.203 × 10¹¹⁰(111-digit number)

72037609656981978949…52056960837475928859

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.440 × 10¹¹¹(112-digit number)

14407521931396395789…04113921674951857719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.881 × 10¹¹¹(112-digit number)

28815043862792791579…08227843349903715439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.763 × 10¹¹¹(112-digit number)

57630087725585583159…16455686699807430879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.152 × 10¹¹²(113-digit number)

11526017545117116631…32911373399614861759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.305 × 10¹¹²(113-digit number)

23052035090234233263…65822746799229723519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.610 × 10¹¹²(113-digit number)

46104070180468466527…31645493598459447039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.220 × 10¹¹²(113-digit number)

92208140360936933055…63290987196918894079

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