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Block #223,786

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/23/2013, 7:04:16 AM Β· Difficulty 9.9376 Β· 6,585,710 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7c27deaf76c9b16f8a7837f636ee29660cff3fa7cfd06f0ec5626fba46441d2b
View on Chainz β†—

Height

#223,786

Difficulty

9.937559

Transactions

2

Size

504 B

Version

2

Bits

09f003e5

Nonce

8,448

Timestamp

10/23/2013, 7:04:16 AM

Confirmations

6,585,710

Mined by

⛏️ P2SHAcook95Ynf9r2PdmuBxW5c3Gx5fGcALPfH

Merkle Root

b57a2b5630a78c240531a3aa7a8779d109dd7e2885448a08d0731c142574b414
Transactions (2)
Coinbasee31ef08b3e13e9…bd6c431152a427
1 in β†’ 1 out10.1200 XPM109 B
Acook95Y…fGcALPfH
24d2332b17e4e9…1c9e00404cfe4a
2 in β†’ 1 out10.2100 XPM306 B
AJfQWJkw…U9BcDBag
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.

1.185 Γ— 10⁹²(93-digit number)
11859074954804178161…88505634020262579279
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
1.185 Γ— 10⁹²(93-digit number)
11859074954804178161…88505634020262579279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.371 Γ— 10⁹²(93-digit number)
23718149909608356322…77011268040525158559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.743 Γ— 10⁹²(93-digit number)
47436299819216712645…54022536081050317119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.487 Γ— 10⁹²(93-digit number)
94872599638433425290…08045072162100634239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.897 Γ— 10⁹³(94-digit number)
18974519927686685058…16090144324201268479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.794 Γ— 10⁹³(94-digit number)
37949039855373370116…32180288648402536959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.589 Γ— 10⁹³(94-digit number)
75898079710746740232…64360577296805073919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.517 Γ— 10⁹⁴(95-digit number)
15179615942149348046…28721154593610147839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.035 Γ— 10⁹⁴(95-digit number)
30359231884298696092…57442309187220295679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.071 Γ— 10⁹⁴(95-digit number)
60718463768597392185…14884618374440591359
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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:57,720,040 XPMΒ·at block #6,809,495 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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