Block #247,666

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/6/2013, 9:39:59 PM · Difficulty 9.9652 · 6,558,383 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bf4105a6672dd7b80e1741059469db5f3267af4f5382067a0a6e9baf96bde3d1

Height

#247,666

Difficulty

9.965233

Transactions

2

Size

452 B

Version

2

Bits

09f71986

Nonce

1,797

Timestamp

11/6/2013, 9:39:59 PM

Confirmations

6,558,383

Merkle Root

fadbadb3c919b2d56f7ae3cf15623f23f7738d0c5474f704287ed2bc3ef0112e
Transactions (2)
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.

1.592 × 10⁹⁴(95-digit number)
15921608768477460724…81558777288874839839
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.

1
origin − 1
1.592 × 10⁹⁴(95-digit number)
15921608768477460724…81558777288874839839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.184 × 10⁹⁴(95-digit number)
31843217536954921449…63117554577749679679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.368 × 10⁹⁴(95-digit number)
63686435073909842898…26235109155499359359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.273 × 10⁹⁵(96-digit number)
12737287014781968579…52470218310998718719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.547 × 10⁹⁵(96-digit number)
25474574029563937159…04940436621997437439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.094 × 10⁹⁵(96-digit number)
50949148059127874318…09880873243994874879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.018 × 10⁹⁶(97-digit number)
10189829611825574863…19761746487989749759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.037 × 10⁹⁶(97-digit number)
20379659223651149727…39523492975979499519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.075 × 10⁹⁶(97-digit number)
40759318447302299455…79046985951958999039
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,692,474 XPM·at block #6,806,048 · updates every 60s
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