Block #670,471

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 8/9/2014, 2:49:15 PM · Difficulty 10.9642 · 6,125,975 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

bec08158ed581f1be973fb31e6672ed66fc02bc98dabcb23128ba9f193a0495a

View on Chainz ↗

Height

#670,471

Difficulty

10.964157

Transactions

Size

4.75 KB

Version

Bits

0af6d2fe

Nonce

1,644,246,428

Timestamp

8/9/2014, 2:49:15 PM

Confirmations

6,125,975

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6eec53bb2824b165b33f2345f491c7641c3158d0f305cc493fd0ac3f4144e079

Transactions (2)

Coinbase046cfcd6ef32c6…8951c80ff1dd7c

1 in → 1 out8.3700 XPM116 B

ANSXnLY2…Sd25TjkD

fbc8395af2741f…68cbc2c9c3c69e

31 in → 2 out898.1003 XPM4.55 KB

ASNpb72b…j7F7nr6F AQgviEqK…FKEYQWHC

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.

1.171 × 10⁹⁸(99-digit number)

11715599921732184908…98125508286940559359

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

1.171 × 10⁹⁸(99-digit number)

11715599921732184908…98125508286940559359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.343 × 10⁹⁸(99-digit number)

23431199843464369817…96251016573881118719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.686 × 10⁹⁸(99-digit number)

46862399686928739634…92502033147762237439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.372 × 10⁹⁸(99-digit number)

93724799373857479268…85004066295524474879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.874 × 10⁹⁹(100-digit number)

18744959874771495853…70008132591048949759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.748 × 10⁹⁹(100-digit number)

37489919749542991707…40016265182097899519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.497 × 10⁹⁹(100-digit number)

74979839499085983414…80032530364195799039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.499 × 10¹⁰⁰(101-digit number)

14995967899817196682…60065060728391598079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.999 × 10¹⁰⁰(101-digit number)

29991935799634393365…20130121456783196159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.998 × 10¹⁰⁰(101-digit number)

59983871599268786731…40260242913566392319

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