Block #2,746,060

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 7/12/2018, 6:21:56 PM · Difficulty 11.6503 · 4,096,433 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6ab926daf8181b5cd670026dadd44e4a30ebe509c30500e8f46a613f1c2469d5

Height

#2,746,060

Difficulty

11.650341

Transactions

5

Size

1.45 KB

Version

2

Bits

0ba67cc6

Nonce

911,691,874

Timestamp

7/12/2018, 6:21:56 PM

Confirmations

4,096,433

Merkle Root

a1043a5e33de3935000a051ad52acaa7d79d88df5095f0aa7359a5362db693ce
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.

9.396 × 10⁹⁷(98-digit number)
93962939721560599986…01421506563217858561
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
9.396 × 10⁹⁷(98-digit number)
93962939721560599986…01421506563217858561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.879 × 10⁹⁸(99-digit number)
18792587944312119997…02843013126435717121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.758 × 10⁹⁸(99-digit number)
37585175888624239994…05686026252871434241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.517 × 10⁹⁸(99-digit number)
75170351777248479988…11372052505742868481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.503 × 10⁹⁹(100-digit number)
15034070355449695997…22744105011485736961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.006 × 10⁹⁹(100-digit number)
30068140710899391995…45488210022971473921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.013 × 10⁹⁹(100-digit number)
60136281421798783991…90976420045942947841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.202 × 10¹⁰⁰(101-digit number)
12027256284359756798…81952840091885895681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.405 × 10¹⁰⁰(101-digit number)
24054512568719513596…63905680183771791361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.810 × 10¹⁰⁰(101-digit number)
48109025137439027192…27811360367543582721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
9.621 × 10¹⁰⁰(101-digit number)
96218050274878054385…55622720735087165441
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:57,984,362 XPM·at block #6,842,492 · updates every 60s
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