Block #444,031

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/14/2014, 11:44:33 PM · Difficulty 10.3439 · 6,381,282 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

bb618ab7cbdf0a2d8703516a2d77d213c37f953ada8b6350fa9dfac3493b190b

View on Chainz ↗

Height

#444,031

Difficulty

10.343867

Transactions

Size

201 B

Version

Bits

0a5807a5

Nonce

347,257

Timestamp

3/14/2014, 11:44:33 PM

Confirmations

6,381,282

Mined by

⛏️ P2SHAT4me1AvZf8VyvR54NxSRAex8obz6JjojW

Merkle Root

2d41b0ec58633468c5f862d60f724880f8e3020c167575e9e4ff3989e1a46aff

Transactions (1)

Coinbase2d41b0ec586334…ff3989e1a46aff

1 in → 1 out9.3300 XPM109 B

AT4me1Av…bz6JjojW

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.

1.037 × 10¹⁰⁰(101-digit number)

10372041724633560543…41223111967449053029

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

1.037 × 10¹⁰⁰(101-digit number)

10372041724633560543…41223111967449053029

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.074 × 10¹⁰⁰(101-digit number)

20744083449267121086…82446223934898106059

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.148 × 10¹⁰⁰(101-digit number)

41488166898534242173…64892447869796212119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.297 × 10¹⁰⁰(101-digit number)

82976333797068484346…29784895739592424239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.659 × 10¹⁰¹(102-digit number)

16595266759413696869…59569791479184848479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.319 × 10¹⁰¹(102-digit number)

33190533518827393738…19139582958369696959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.638 × 10¹⁰¹(102-digit number)

66381067037654787476…38279165916739393919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.327 × 10¹⁰²(103-digit number)

13276213407530957495…76558331833478787839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.655 × 10¹⁰²(103-digit number)

26552426815061914990…53116663666957575679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.310 × 10¹⁰²(103-digit number)

53104853630123829981…06233327333915151359

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 #444,031

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