Block #2,490,110

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/25/2018, 8:58:00 PM · Difficulty 10.9706 · 4,352,164 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9008bd7cd0218fe948b01051498c7a2b0fa07bf3eecc5ca72ae6b9adb15139fd

Height

#2,490,110

Difficulty

10.970621

Transactions

2

Size

722 B

Version

2

Bits

0af87aa4

Nonce

1,279,370,976

Timestamp

1/25/2018, 8:58:00 PM

Confirmations

4,352,164

Merkle Root

7f7c65b20caa35ece6fb9c0183fcd3f56df6eb3b00d8adc3a433dd29d923854c
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.

4.073 × 10⁹⁵(96-digit number)
40732118127598571112…90602834546531498241
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
4.073 × 10⁹⁵(96-digit number)
40732118127598571112…90602834546531498241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.146 × 10⁹⁵(96-digit number)
81464236255197142224…81205669093062996481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.629 × 10⁹⁶(97-digit number)
16292847251039428444…62411338186125992961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.258 × 10⁹⁶(97-digit number)
32585694502078856889…24822676372251985921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.517 × 10⁹⁶(97-digit number)
65171389004157713779…49645352744503971841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.303 × 10⁹⁷(98-digit number)
13034277800831542755…99290705489007943681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.606 × 10⁹⁷(98-digit number)
26068555601663085511…98581410978015887361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.213 × 10⁹⁷(98-digit number)
52137111203326171023…97162821956031774721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.042 × 10⁹⁸(99-digit number)
10427422240665234204…94325643912063549441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.085 × 10⁹⁸(99-digit number)
20854844481330468409…88651287824127098881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.170 × 10⁹⁸(99-digit number)
41709688962660936818…77302575648254197761
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:57,982,593 XPM·at block #6,842,273 · updates every 60s
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