Block #600,247

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/24/2014, 1:51:41 PM · Difficulty 10.9181 · 6,209,165 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

7bf2d8a25ff7d7e78c466bf6208f85b763913619219a9795a22f41ccc0cf86e6

View on Chainz ↗

Height

#600,247

Difficulty

10.918081

Transactions

Size

561 B

Version

Bits

0aeb0754

Nonce

47,105

Timestamp

6/24/2014, 1:51:41 PM

Confirmations

6,209,165

Mined by

⛏️ aS}AJzWx2VDShfKP9pKK3jZqTbn4sj4ZSMit5

Merkle Root

4f300f174d018f9aeadd4423e3911e6d6d30c53e80bc659bf4021518f3c2b056

Transactions (1)

Coinbase4f300f174d018f…021518f3c2b056

1 in → 12 out8.3800 XPM471 B

AJzWx2VD…j4ZSMit5 AJtNW28X…Syb4Ph5j AQvZBsUo…hppgRZTJ AQyr8Lw3…hs4nt3Pn AJtsGkR4…BuZ5GKQN

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.

4.171 × 10⁹³(94-digit number)

41719704774949988483…72603138044522475519

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

4.171 × 10⁹³(94-digit number)

41719704774949988483…72603138044522475519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.343 × 10⁹³(94-digit number)

83439409549899976967…45206276089044951039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.668 × 10⁹⁴(95-digit number)

16687881909979995393…90412552178089902079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.337 × 10⁹⁴(95-digit number)

33375763819959990787…80825104356179804159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.675 × 10⁹⁴(95-digit number)

66751527639919981574…61650208712359608319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.335 × 10⁹⁵(96-digit number)

13350305527983996314…23300417424719216639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.670 × 10⁹⁵(96-digit number)

26700611055967992629…46600834849438433279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.340 × 10⁹⁵(96-digit number)

53401222111935985259…93201669698876866559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.068 × 10⁹⁶(97-digit number)

10680244422387197051…86403339397753733119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.136 × 10⁹⁶(97-digit number)

21360488844774394103…72806678795507466239

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 #600,247

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