Block #48,421

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/15/2013, 3:15:05 PM · Difficulty 8.8444 · 6,776,960 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

13c23fde7a80b971c8ed256f38aed80aa5793fdc0276b80481d4a34bc76250f4

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Height

#48,421

Difficulty

8.844447

Transactions

Size

208 B

Version

Bits

08d82db2

Nonce

747

Timestamp

7/15/2013, 3:15:05 PM

Confirmations

6,776,960

Mined by

⛏️ P2SHAV9qaqUGdFf78UYdPZSBksGR5qjFgzaVCh

Merkle Root

fa3373deb6c579d98cbfd966d6ad6d8e454e375130b5a5c6881545b09e543b5b

Transactions (1)

Coinbasefa3373deb6c579…1545b09e543b5b

1 in → 1 out12.7700 XPM110 B

AV9qaqUG…jFgzaVCh

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.

1.057 × 10¹¹³(114-digit number)

10574974690375755562…13935513669284650121

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

1.057 × 10¹¹³(114-digit number)

10574974690375755562…13935513669284650121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.114 × 10¹¹³(114-digit number)

21149949380751511125…27871027338569300241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.229 × 10¹¹³(114-digit number)

42299898761503022250…55742054677138600481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.459 × 10¹¹³(114-digit number)

84599797523006044500…11484109354277200961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.691 × 10¹¹⁴(115-digit number)

16919959504601208900…22968218708554401921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.383 × 10¹¹⁴(115-digit number)

33839919009202417800…45936437417108803841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.767 × 10¹¹⁴(115-digit number)

67679838018404835600…91872874834217607681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.353 × 10¹¹⁵(116-digit number)

13535967603680967120…83745749668435215361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.707 × 10¹¹⁵(116-digit number)

27071935207361934240…67491499336870430721

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the Second 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer

Block #48,421

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