Block #1,449,721

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/9/2016, 8:03:25 PM · Difficulty 10.7537 · 5,392,243 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c125375a7b53efda9b988a61a46e91bb9f2b9cb5d2c8ba2e2a3b1d978df0e098

Height

#1,449,721

Difficulty

10.753677

Transactions

2

Size

1.21 KB

Version

2

Bits

0ac0f0fc

Nonce

253,547,123

Timestamp

2/9/2016, 8:03:25 PM

Confirmations

5,392,243

Merkle Root

aa6ad22d7807444c3d4e7a03b7010b2c6e1af0f0f6ae1220b4ebfc7edd8c41e5
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.

6.492 × 10⁹⁴(95-digit number)
64924040748862765033…26600186014894504801
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
6.492 × 10⁹⁴(95-digit number)
64924040748862765033…26600186014894504801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.298 × 10⁹⁵(96-digit number)
12984808149772553006…53200372029789009601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.596 × 10⁹⁵(96-digit number)
25969616299545106013…06400744059578019201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.193 × 10⁹⁵(96-digit number)
51939232599090212026…12801488119156038401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.038 × 10⁹⁶(97-digit number)
10387846519818042405…25602976238312076801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.077 × 10⁹⁶(97-digit number)
20775693039636084810…51205952476624153601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.155 × 10⁹⁶(97-digit number)
41551386079272169621…02411904953248307201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.310 × 10⁹⁶(97-digit number)
83102772158544339242…04823809906496614401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.662 × 10⁹⁷(98-digit number)
16620554431708867848…09647619812993228801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.324 × 10⁹⁷(98-digit number)
33241108863417735697…19295239625986457601
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:57,980,094 XPM·at block #6,841,963 · updates every 60s
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