Block #998,674

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/1/2015, 3:30:02 PM · Difficulty 10.7932 · 5,826,356 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
84edfa8f2b158d51b29c3a229a8c2b434995b10a2ef147680447a1682130c637

Height

#998,674

Difficulty

10.793220

Transactions

4

Size

1.58 KB

Version

2

Bits

0acb1070

Nonce

653,829,867

Timestamp

4/1/2015, 3:30:02 PM

Confirmations

5,826,356

Merkle Root

51da3f6604635486fc0cd69c6b1063daf1bc559d1f827a87d9cf0381453251f3
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.

6.451 × 10⁹⁴(95-digit number)
64518551862917453073…64481560072714967041
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
6.451 × 10⁹⁴(95-digit number)
64518551862917453073…64481560072714967041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.290 × 10⁹⁵(96-digit number)
12903710372583490614…28963120145429934081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.580 × 10⁹⁵(96-digit number)
25807420745166981229…57926240290859868161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.161 × 10⁹⁵(96-digit number)
51614841490333962458…15852480581719736321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.032 × 10⁹⁶(97-digit number)
10322968298066792491…31704961163439472641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.064 × 10⁹⁶(97-digit number)
20645936596133584983…63409922326878945281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.129 × 10⁹⁶(97-digit number)
41291873192267169966…26819844653757890561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.258 × 10⁹⁶(97-digit number)
82583746384534339933…53639689307515781121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.651 × 10⁹⁷(98-digit number)
16516749276906867986…07279378615031562241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.303 × 10⁹⁷(98-digit number)
33033498553813735973…14558757230063124481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
6.606 × 10⁹⁷(98-digit number)
66066997107627471946…29117514460126248961
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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, …
Circulating Supply:57,844,323 XPM·at block #6,825,029 · updates every 60s
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