Block #371,617

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/23/2014, 12:19:53 AM · Difficulty 10.4319 · 6,422,844 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e7b6a7941d9a325173f8106dfffdb2e00655b3eb21f244ffc74fcc56785a5f2d

Height

#371,617

Difficulty

10.431912

Transactions

5

Size

1.37 KB

Version

2

Bits

0a6e91cf

Nonce

58,613

Timestamp

1/23/2014, 12:19:53 AM

Confirmations

6,422,844

Merkle Root

f72803d1e06f3d6b7901bd796205d0368ef150629f716fe2c9f34b8929914647
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.

5.093 × 10⁹⁸(99-digit number)
50932423915208469024…59972193953724324479
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
5.093 × 10⁹⁸(99-digit number)
50932423915208469024…59972193953724324479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.018 × 10⁹⁹(100-digit number)
10186484783041693804…19944387907448648959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.037 × 10⁹⁹(100-digit number)
20372969566083387609…39888775814897297919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.074 × 10⁹⁹(100-digit number)
40745939132166775219…79777551629794595839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
8.149 × 10⁹⁹(100-digit number)
81491878264333550439…59555103259589191679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.629 × 10¹⁰⁰(101-digit number)
16298375652866710087…19110206519178383359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.259 × 10¹⁰⁰(101-digit number)
32596751305733420175…38220413038356766719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.519 × 10¹⁰⁰(101-digit number)
65193502611466840351…76440826076713533439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.303 × 10¹⁰¹(102-digit number)
13038700522293368070…52881652153427066879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.607 × 10¹⁰¹(102-digit number)
26077401044586736140…05763304306854133759
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:57,599,729 XPM·at block #6,794,460 · updates every 60s
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