Block #207,980

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/13/2013, 6:05:24 PM · Difficulty 9.9048 · 6,586,662 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c9f9c565aedf3b7ff73953da659dba46ab06a2acd0f37d98aca6de395e737f4c

Height

#207,980

Difficulty

9.904800

Transactions

3

Size

584 B

Version

2

Bits

09e7a0f3

Nonce

24,190

Timestamp

10/13/2013, 6:05:24 PM

Confirmations

6,586,662

Merkle Root

d8fec05f42041f130b01cc1c0fdc4fc02917bd92948bd586bcdb2367279b6f23
Transactions (3)
1 in → 1 out10.2000 XPM109 B
1 in → 1 out499.9900 XPM192 B
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.

9.389 × 10⁹⁵(96-digit number)
93891497956813866965…60571676859974960079
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
9.389 × 10⁹⁵(96-digit number)
93891497956813866965…60571676859974960079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.877 × 10⁹⁶(97-digit number)
18778299591362773393…21143353719949920159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.755 × 10⁹⁶(97-digit number)
37556599182725546786…42286707439899840319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.511 × 10⁹⁶(97-digit number)
75113198365451093572…84573414879799680639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.502 × 10⁹⁷(98-digit number)
15022639673090218714…69146829759599361279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.004 × 10⁹⁷(98-digit number)
30045279346180437429…38293659519198722559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.009 × 10⁹⁷(98-digit number)
60090558692360874858…76587319038397445119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.201 × 10⁹⁸(99-digit number)
12018111738472174971…53174638076794890239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.403 × 10⁹⁸(99-digit number)
24036223476944349943…06349276153589780479
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,601,183 XPM·at block #6,794,641 · updates every 60s
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