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Block #216,620

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/18/2013, 8:12:41 PM Β· Difficulty 9.9271 Β· 6,579,067 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
091b9bf56b8299f5c256ab60a617ff9cae0101b9ec1735d69f30f262d7d5e1ce
View on Chainz β†—

Height

#216,620

Difficulty

9.927085

Transactions

2

Size

1.14 KB

Version

2

Bits

09ed5569

Nonce

142,802

Timestamp

10/18/2013, 8:12:41 PM

Confirmations

6,579,067

Mined by

⛏️ P2SHAZY8QvBkSkxnhLcCWcB4ZHyTMhH6KaAkjX

Merkle Root

09f6b9818c730f838bc2552ddc08b874077f7e31e593604e8522ec8b10634aa3
Transactions (2)
Coinbasedb9dde5e20028a…ec3eb5ee1f598c
1 in β†’ 1 out10.1400 XPM109 B
AZY8QvBk…H6KaAkjX
563390bd99a29a…795da04eb3a787
6 in β†’ 2 out1147.6100 XPM966 B
AFqDj4vn…D3w8GBCwAKLG68c3…1twkWboo
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.258 Γ— 10⁹²(93-digit number)
72587946660636112550…62974699722270342399
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
7.258 Γ— 10⁹²(93-digit number)
72587946660636112550…62974699722270342399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.451 Γ— 10⁹³(94-digit number)
14517589332127222510…25949399444540684799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.903 Γ— 10⁹³(94-digit number)
29035178664254445020…51898798889081369599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.807 Γ— 10⁹³(94-digit number)
58070357328508890040…03797597778162739199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.161 Γ— 10⁹⁴(95-digit number)
11614071465701778008…07595195556325478399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.322 Γ— 10⁹⁴(95-digit number)
23228142931403556016…15190391112650956799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.645 Γ— 10⁹⁴(95-digit number)
46456285862807112032…30380782225301913599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.291 Γ— 10⁹⁴(95-digit number)
92912571725614224064…60761564450603827199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.858 Γ— 10⁹⁡(96-digit number)
18582514345122844812…21523128901207654399
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,609,565 XPMΒ·at block #6,795,686 Β· updates every 60s
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