Block #1,449,974

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/10/2016, 1:04:49 AM · Difficulty 10.7513 · 5,392,053 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
db59dceac1a1487ced551f63df57f3f2b3cb169219e152f8f9258a7dd2b993d6

Height

#1,449,974

Difficulty

10.751329

Transactions

2

Size

833 B

Version

2

Bits

0ac0571e

Nonce

798,521,936

Timestamp

2/10/2016, 1:04:49 AM

Confirmations

5,392,053

Merkle Root

891247fdecc9996d9e12e7e73d7ab3bf4e000273dcd942bf06382710de859897
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.

7.067 × 10⁹⁴(95-digit number)
70672851933933392166…61257728280029978801
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
7.067 × 10⁹⁴(95-digit number)
70672851933933392166…61257728280029978801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.413 × 10⁹⁵(96-digit number)
14134570386786678433…22515456560059957601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.826 × 10⁹⁵(96-digit number)
28269140773573356866…45030913120119915201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.653 × 10⁹⁵(96-digit number)
56538281547146713733…90061826240239830401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.130 × 10⁹⁶(97-digit number)
11307656309429342746…80123652480479660801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.261 × 10⁹⁶(97-digit number)
22615312618858685493…60247304960959321601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.523 × 10⁹⁶(97-digit number)
45230625237717370986…20494609921918643201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.046 × 10⁹⁶(97-digit number)
90461250475434741973…40989219843837286401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.809 × 10⁹⁷(98-digit number)
18092250095086948394…81978439687674572801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.618 × 10⁹⁷(98-digit number)
36184500190173896789…63956879375349145601
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,980,602 XPM·at block #6,842,026 · updates every 60s
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