Block #298,472

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 12/7/2013, 8:49:23 AM · Difficulty 9.9919 · 6,505,233 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

87e341e7c50af3425c4efe3c8635cd7274f03544c83b3eadf6ae67abcdf5e3e5

View on Chainz ↗

Height

#298,472

Difficulty

9.991936

Transactions

Size

1.11 KB

Version

Bits

09fdef7d

Nonce

25,753

Timestamp

12/7/2013, 8:49:23 AM

Confirmations

6,505,233

Mined by

⛏️ aRAZ2pPuKgN7GXPJPBLxtm9bkWcE95SN2Yr7

Merkle Root

52dc346699ca92370030b582de3283b84c3a118b0a25c5abe5d6e1bfa89389bd

Transactions (1)

Coinbase52dc346699ca92…d6e1bfa89389bd

1 in → 29 out9.9800 XPM1.02 KB

AZ2pPuKg…95SN2Yr7 APeshfYV…3PKcKMKH AHuJ9wYh…BGmgHrKZ AYcLTeXR…bscgPops 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.

4.767 × 10⁹³(94-digit number)

47671588934692120827…12171037195374842559

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

4.767 × 10⁹³(94-digit number)

47671588934692120827…12171037195374842559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

9.534 × 10⁹³(94-digit number)

95343177869384241654…24342074390749685119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.906 × 10⁹⁴(95-digit number)

19068635573876848330…48684148781499370239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.813 × 10⁹⁴(95-digit number)

38137271147753696661…97368297562998740479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.627 × 10⁹⁴(95-digit number)

76274542295507393323…94736595125997480959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.525 × 10⁹⁵(96-digit number)

15254908459101478664…89473190251994961919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.050 × 10⁹⁵(96-digit number)

30509816918202957329…78946380503989923839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.101 × 10⁹⁵(96-digit number)

61019633836405914659…57892761007979847679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.220 × 10⁹⁶(97-digit number)

12203926767281182931…15785522015959695359

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