Block #672,647

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 8/11/2014, 1:35:00 AM · Difficulty 10.9649 · 6,135,578 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1a4cec2c3a11395fdd08d7e9c3508e0be903e61bb5ae74ee6cff1f90f72e1389

Height

#672,647

Difficulty

10.964855

Transactions

3

Size

954 B

Version

2

Bits

0af700c5

Nonce

564,022,602

Timestamp

8/11/2014, 1:35:00 AM

Confirmations

6,135,578

Merkle Root

019f5b73a0bfc408a75512701cd0fef5749362f8b0774dfb3fef57162c610ab5
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.

4.664 × 10⁹⁶(97-digit number)
46641583023373030255…36511802128492981759
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
4.664 × 10⁹⁶(97-digit number)
46641583023373030255…36511802128492981759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.328 × 10⁹⁶(97-digit number)
93283166046746060510…73023604256985963519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.865 × 10⁹⁷(98-digit number)
18656633209349212102…46047208513971927039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.731 × 10⁹⁷(98-digit number)
37313266418698424204…92094417027943854079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.462 × 10⁹⁷(98-digit number)
74626532837396848408…84188834055887708159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.492 × 10⁹⁸(99-digit number)
14925306567479369681…68377668111775416319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.985 × 10⁹⁸(99-digit number)
29850613134958739363…36755336223550832639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.970 × 10⁹⁸(99-digit number)
59701226269917478726…73510672447101665279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.194 × 10⁹⁹(100-digit number)
11940245253983495745…47021344894203330559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.388 × 10⁹⁹(100-digit number)
23880490507966991490…94042689788406661119
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:57,709,852 XPM·at block #6,808,224 · updates every 60s
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