Block #1,478,597

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/1/2016, 11:13:24 AM · Difficulty 10.7104 · 5,365,443 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
95a9a442431a8d6cf545819b7064b871444eafbcf74a62ffd9a449bbdcaa19b2

Height

#1,478,597

Difficulty

10.710420

Transactions

1

Size

243 B

Version

2

Bits

0ab5de12

Nonce

425,159,330

Timestamp

3/1/2016, 11:13:24 AM

Confirmations

5,365,443

Merkle Root

1b1389dafc8ee7f3c0b0437180c876a2f28e009e1ca2c0b054441fd1949a369c
Transactions (1)
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.

3.017 × 10⁹⁷(98-digit number)
30178136576980753008…76417566983183308801
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
3.017 × 10⁹⁷(98-digit number)
30178136576980753008…76417566983183308801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.035 × 10⁹⁷(98-digit number)
60356273153961506017…52835133966366617601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.207 × 10⁹⁸(99-digit number)
12071254630792301203…05670267932733235201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.414 × 10⁹⁸(99-digit number)
24142509261584602406…11340535865466470401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.828 × 10⁹⁸(99-digit number)
48285018523169204813…22681071730932940801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.657 × 10⁹⁸(99-digit number)
96570037046338409627…45362143461865881601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.931 × 10⁹⁹(100-digit number)
19314007409267681925…90724286923731763201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.862 × 10⁹⁹(100-digit number)
38628014818535363851…81448573847463526401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.725 × 10⁹⁹(100-digit number)
77256029637070727702…62897147694927052801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.545 × 10¹⁰⁰(101-digit number)
15451205927414145540…25794295389854105601
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:57,996,689 XPM·at block #6,844,039 · updates every 60s
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