Block #911,305

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/27/2015, 12:07:12 AM · Difficulty 10.9314 · 5,882,836 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

21fd948a99728c54d1141c61842ce6216921d79f4c4b63f70e75642179379fda

View on Chainz ↗

Height

#911,305

Difficulty

10.931400

Transactions

Size

1.54 KB

Version

Bits

0aee7033

Nonce

40,431,834

Timestamp

1/27/2015, 12:07:12 AM

Confirmations

5,882,836

Merkle Root

c152cba0a0d8e1b5a0e5280a615588727e329be4ec2203243a2dcf8fa73d889e

Transactions (2)

Coinbase7ee538737fd1e1…b1d4021b64fbe3

1 in → 1 out8.3800 XPM109 B

AW6rpG8k…57KTfFns

f0504b17c4b533…ee11251db88fa6

9 in → 1 out738.4200 XPM1.35 KB

AQ3SuyCM…AmNvneTb

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.

1.680 × 10⁹⁴(95-digit number)

16803684944006620648…09179531429804422579

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

1.680 × 10⁹⁴(95-digit number)

16803684944006620648…09179531429804422579

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.360 × 10⁹⁴(95-digit number)

33607369888013241297…18359062859608845159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.721 × 10⁹⁴(95-digit number)

67214739776026482595…36718125719217690319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.344 × 10⁹⁵(96-digit number)

13442947955205296519…73436251438435380639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.688 × 10⁹⁵(96-digit number)

26885895910410593038…46872502876870761279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.377 × 10⁹⁵(96-digit number)

53771791820821186076…93745005753741522559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.075 × 10⁹⁶(97-digit number)

10754358364164237215…87490011507483045119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.150 × 10⁹⁶(97-digit number)

21508716728328474430…74980023014966090239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.301 × 10⁹⁶(97-digit number)

43017433456656948861…49960046029932180479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.603 × 10⁹⁶(97-digit number)

86034866913313897722…99920092059864360959

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