Block #299,472

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/7/2013, 11:55:30 PM · Difficulty 9.9921 · 6,510,156 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b4c60f910019236a3803496849e941490a643a88f92114ea3f883bbe7ec3cfd0

View on Chainz ↗

Height

#299,472

Difficulty

9.992130

Transactions

Size

799 B

Version

Bits

09fdfc3a

Nonce

55,478

Timestamp

12/7/2013, 11:55:30 PM

Confirmations

6,510,156

Mined by

⛏️ aRpAbWryTLppYzT7YQH9f3KnXDN6y2k7co546

Merkle Root

edc9205720cfbb284da0ef84e971cde2af369cf6b65a00b867acd2d5644ce3e4

Transactions (1)

Coinbaseedc9205720cfbb…acd2d5644ce3e4

1 in → 19 out10.0000 XPM709 B

AbWryTLp…2k7co546 AMdvB6BS…DPq9FYdA AX2VaXup…gXWCNRYT AQwRN8bE…V8PsTcY9 Ad9pSzHt…cpJ3y2zz

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.

1.175 × 10⁹⁴(95-digit number)

11751416418215929577…50728772952998401919

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

1.175 × 10⁹⁴(95-digit number)

11751416418215929577…50728772952998401919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.350 × 10⁹⁴(95-digit number)

23502832836431859154…01457545905996803839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.700 × 10⁹⁴(95-digit number)

47005665672863718308…02915091811993607679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.401 × 10⁹⁴(95-digit number)

94011331345727436616…05830183623987215359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.880 × 10⁹⁵(96-digit number)

18802266269145487323…11660367247974430719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.760 × 10⁹⁵(96-digit number)

37604532538290974646…23320734495948861439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.520 × 10⁹⁵(96-digit number)

75209065076581949293…46641468991897722879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.504 × 10⁹⁶(97-digit number)

15041813015316389858…93282937983795445759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.008 × 10⁹⁶(97-digit number)

30083626030632779717…86565875967590891519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.016 × 10⁹⁶(97-digit number)

60167252061265559434…73131751935181783039

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

Block #299,472

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