Block #2,660,062

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/14/2018, 3:06:58 AM · Difficulty 11.6386 · 4,184,713 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7178d7801e297a69ddcfb68b97da895c4e04b4c68b531c63d3cb41349b941a32

Height

#2,660,062

Difficulty

11.638595

Transactions

1

Size

201 B

Version

2

Bits

0ba37afb

Nonce

790,681,777

Timestamp

5/14/2018, 3:06:58 AM

Confirmations

4,184,713

Merkle Root

4b555f4f49f49a7eb7fdaf695120faae1050c156a59a95c37cafdfea59fa5c13
Transactions (1)
1 in → 1 out7.3700 XPM110 B
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.

1.214 × 10⁹⁶(97-digit number)
12144696400626334400…88235353833576370561
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
1.214 × 10⁹⁶(97-digit number)
12144696400626334400…88235353833576370561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.428 × 10⁹⁶(97-digit number)
24289392801252668801…76470707667152741121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.857 × 10⁹⁶(97-digit number)
48578785602505337602…52941415334305482241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.715 × 10⁹⁶(97-digit number)
97157571205010675205…05882830668610964481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.943 × 10⁹⁷(98-digit number)
19431514241002135041…11765661337221928961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.886 × 10⁹⁷(98-digit number)
38863028482004270082…23531322674443857921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.772 × 10⁹⁷(98-digit number)
77726056964008540164…47062645348887715841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.554 × 10⁹⁸(99-digit number)
15545211392801708032…94125290697775431681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.109 × 10⁹⁸(99-digit number)
31090422785603416065…88250581395550863361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.218 × 10⁹⁸(99-digit number)
62180845571206832131…76501162791101726721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.243 × 10⁹⁹(100-digit number)
12436169114241366426…53002325582203453441
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:58,002,610 XPM·at block #6,844,774 · updates every 60s
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