Block #348,551

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/7/2014, 8:51:32 PM · Difficulty 10.2615 · 6,460,934 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f538bbf71c97b5e8b96f64646e6e4a8ddd0d4c51a0bb942608f069b44c371479

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Height

#348,551

Difficulty

10.261484

Transactions

Size

1.05 KB

Version

Bits

0a42f0a3

Nonce

3,993

Timestamp

1/7/2014, 8:51:32 PM

Confirmations

6,460,934

Mined by

⛏️ QaRh*Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

ed60f7d69a5e4f239c5c5f5555eed6e4c7dcbe88736b559a81e953fb74f8b05d

Transactions (1)

Coinbaseed60f7d69a5e4f…e953fb74f8b05d

1 in → 27 out9.4800 XPM981 B

Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AUnkFe8H…fvenjA4X AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz

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.

5.737 × 10⁹³(94-digit number)

57378637282461915698…47694267138786313759

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

5.737 × 10⁹³(94-digit number)

57378637282461915698…47694267138786313759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.147 × 10⁹⁴(95-digit number)

11475727456492383139…95388534277572627519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.295 × 10⁹⁴(95-digit number)

22951454912984766279…90777068555145255039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.590 × 10⁹⁴(95-digit number)

45902909825969532559…81554137110290510079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.180 × 10⁹⁴(95-digit number)

91805819651939065118…63108274220581020159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.836 × 10⁹⁵(96-digit number)

18361163930387813023…26216548441162040319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.672 × 10⁹⁵(96-digit number)

36722327860775626047…52433096882324080639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.344 × 10⁹⁵(96-digit number)

73444655721551252094…04866193764648161279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.468 × 10⁹⁶(97-digit number)

14688931144310250418…09732387529296322559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.937 × 10⁹⁶(97-digit number)

29377862288620500837…19464775058592645119

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 #348,551

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