Block #375,866

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/26/2014, 12:45:12 AM · Difficulty 10.4229 · 6,451,054 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

47431ada49b718848b1145689f2ad0b3d4b23aaa44abbaf627da88aab3d6e8aa

View on Chainz ↗

Height

#375,866

Difficulty

10.422929

Transactions

Size

210 B

Version

Bits

0a6c450b

Nonce

6,756

Timestamp

1/26/2014, 12:45:12 AM

Confirmations

6,451,054

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

67a59670e566298fbef38fa6bf9028b734492ef64db9c5b5aad55d9d7240b45f

Transactions (1)

Coinbase67a59670e56629…d55d9d7240b45f

1 in → 1 out9.1900 XPM116 B

AbwWkWZt…kawDhufa

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.

1.567 × 10¹⁰⁴(105-digit number)

15678312832018694141…90351592435800556159

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

1.567 × 10¹⁰⁴(105-digit number)

15678312832018694141…90351592435800556159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.135 × 10¹⁰⁴(105-digit number)

31356625664037388283…80703184871601112319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.271 × 10¹⁰⁴(105-digit number)

62713251328074776566…61406369743202224639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.254 × 10¹⁰⁵(106-digit number)

12542650265614955313…22812739486404449279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.508 × 10¹⁰⁵(106-digit number)

25085300531229910626…45625478972808898559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.017 × 10¹⁰⁵(106-digit number)

50170601062459821252…91250957945617797119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.003 × 10¹⁰⁶(107-digit number)

10034120212491964250…82501915891235594239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.006 × 10¹⁰⁶(107-digit number)

20068240424983928501…65003831782471188479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.013 × 10¹⁰⁶(107-digit number)

40136480849967857002…30007663564942376959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.027 × 10¹⁰⁶(107-digit number)

80272961699935714004…60015327129884753919

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 #375,866

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