Block #373,159

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/24/2014, 3:06:20 AM · Difficulty 10.4247 · 6,419,424 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ea9b1a67966e0af4d3fe4c794962748ed239f47e4e84eb53800cd12b168e30a2

Height

#373,159

Difficulty

10.424706

Transactions

2

Size

721 B

Version

2

Bits

0a6cb98a

Nonce

1,052

Timestamp

1/24/2014, 3:06:20 AM

Confirmations

6,419,424

Merkle Root

69358c7bf0f4e506c39a406bca0df90f5e8f916a27755229944122e6d2757e14
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.

3.523 × 10⁹⁹(100-digit number)
35239151694097384317…93723379083543235359
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
3.523 × 10⁹⁹(100-digit number)
35239151694097384317…93723379083543235359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.047 × 10⁹⁹(100-digit number)
70478303388194768635…87446758167086470719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.409 × 10¹⁰⁰(101-digit number)
14095660677638953727…74893516334172941439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.819 × 10¹⁰⁰(101-digit number)
28191321355277907454…49787032668345882879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.638 × 10¹⁰⁰(101-digit number)
56382642710555814908…99574065336691765759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.127 × 10¹⁰¹(102-digit number)
11276528542111162981…99148130673383531519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.255 × 10¹⁰¹(102-digit number)
22553057084222325963…98296261346767063039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.510 × 10¹⁰¹(102-digit number)
45106114168444651926…96592522693534126079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.021 × 10¹⁰¹(102-digit number)
90212228336889303853…93185045387068252159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.804 × 10¹⁰²(103-digit number)
18042445667377860770…86370090774136504319
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,584,633 XPM·at block #6,792,582 · updates every 60s
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