Block #291,387

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/3/2013, 4:02:04 AM · Difficulty 9.9898 · 6,509,420 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

4afb1e6d92eeaa4bf697fa62bef293f702401c3d4033ca2329952172a7f6e7a3

View on Chainz ↗

Height

#291,387

Difficulty

9.989824

Transactions

Size

868 B

Version

Bits

09fd6521

Nonce

66,187

Timestamp

12/3/2013, 4:02:04 AM

Confirmations

6,509,420

Mined by

⛏️ P2SHAXKgkkDGrogBEHJHSetHJnSBPfJyE5mk6Y

Merkle Root

85b2f8d926e1c421370a26462d328dd11886a0eb40fd64edf0e3d932382ed5b5

Transactions (2)

Coinbaseea1dc8c0f1a8b5…01258374f02100

1 in → 1 out10.0200 XPM109 B

AXKgkkDG…JyE5mk6Y

c9dfbc53c3026a…8762c68d91b5d1

4 in → 2 out20.0322 XPM669 B

AWtWttYy…umRkFMGw AYeoqniv…w4ZtxAc1

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.

9.661 × 10⁹³(94-digit number)

96619653489439561182…33590666033079999999

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

9.661 × 10⁹³(94-digit number)

96619653489439561182…33590666033079999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.932 × 10⁹⁴(95-digit number)

19323930697887912236…67181332066159999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.864 × 10⁹⁴(95-digit number)

38647861395775824472…34362664132319999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.729 × 10⁹⁴(95-digit number)

77295722791551648945…68725328264639999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.545 × 10⁹⁵(96-digit number)

15459144558310329789…37450656529279999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.091 × 10⁹⁵(96-digit number)

30918289116620659578…74901313058559999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.183 × 10⁹⁵(96-digit number)

61836578233241319156…49802626117119999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.236 × 10⁹⁶(97-digit number)

12367315646648263831…99605252234239999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.473 × 10⁹⁶(97-digit number)

24734631293296527662…99210504468479999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.946 × 10⁹⁶(97-digit number)

49469262586593055325…98421008936959999999

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