Block #410,247

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/18/2014, 10:47:38 PM · Difficulty 10.4279 · 6,391,555 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e2061d383ac989749d1647df7a7ec81a1186c6be113f8ea80b05b028fc9d6d33

View on Chainz ↗

Height

#410,247

Difficulty

10.427855

Transactions

Size

832 B

Version

Bits

0a6d87e5

Nonce

2,414

Timestamp

2/18/2014, 10:47:38 PM

Confirmations

6,391,555

Mined by

⛏️ BaSAGKhfQo2gx6heCfNgerzn5qmLLh7fBXLX6

Merkle Root

2f00d80d63622a231aa6e1653eb897946562d19313fc01168793bf0a44f8c567

Transactions (1)

Coinbase2f00d80d63622a…93bf0a44f8c567

1 in → 20 out9.1800 XPM743 B

AGKhfQo2…h7fBXLX6 AYtDvcGs…VuAcA7m7 Aac9Hjdg…P4ktypc3 AP5UvYhU…vLTDwkdA ATKK7iFz…wZm46KN1

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.

2.234 × 10⁹³(94-digit number)

22349435791629583720…39981354862637256599

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

2.234 × 10⁹³(94-digit number)

22349435791629583720…39981354862637256599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.469 × 10⁹³(94-digit number)

44698871583259167440…79962709725274513199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.939 × 10⁹³(94-digit number)

89397743166518334880…59925419450549026399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.787 × 10⁹⁴(95-digit number)

17879548633303666976…19850838901098052799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.575 × 10⁹⁴(95-digit number)

35759097266607333952…39701677802196105599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.151 × 10⁹⁴(95-digit number)

71518194533214667904…79403355604392211199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.430 × 10⁹⁵(96-digit number)

14303638906642933580…58806711208784422399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.860 × 10⁹⁵(96-digit number)

28607277813285867161…17613422417568844799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.721 × 10⁹⁵(96-digit number)

57214555626571734323…35226844835137689599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.144 × 10⁹⁶(97-digit number)

11442911125314346864…70453689670275379199

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