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Block #163,469

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/14/2013, 12:30:18 AM Β· Difficulty 9.8620 Β· 6,632,508 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8e48b6f2d19f2e70f86b8a88c2cae86c6fc298f600db3e76e56887ba4125e40f
View on Chainz β†—

Height

#163,469

Difficulty

9.861964

Transactions

2

Size

654 B

Version

2

Bits

09dca9a7

Nonce

56,351

Timestamp

9/14/2013, 12:30:18 AM

Confirmations

6,632,508

Mined by

⛏️ P2SHAdDUNTYmz3S4v6JdhjgL2fyWhUv4Zjqa77

Merkle Root

ab670686c6fa136cc53f63d4b51218c0143c9a3d4832ed5e056115c3631fb879
Transactions (2)
Coinbase553bc77bde1d02…0a6c71fb4a6966
1 in β†’ 1 out10.2800 XPM109 B
AdDUNTYm…v4Zjqa77
30fe6f34985382…8c2f93241bc802
3 in β†’ 2 out21.0800 XPM455 B
AXwhdehU…dQh1B8YnAFz9fXym…wh4UqpkL
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.

4.414 Γ— 10⁹⁴(95-digit number)
44145451419686552283…79023129745138150399
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
4.414 Γ— 10⁹⁴(95-digit number)
44145451419686552283…79023129745138150399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.829 Γ— 10⁹⁴(95-digit number)
88290902839373104566…58046259490276300799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.765 Γ— 10⁹⁡(96-digit number)
17658180567874620913…16092518980552601599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.531 Γ— 10⁹⁡(96-digit number)
35316361135749241826…32185037961105203199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.063 Γ— 10⁹⁡(96-digit number)
70632722271498483653…64370075922210406399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.412 Γ— 10⁹⁢(97-digit number)
14126544454299696730…28740151844420812799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.825 Γ— 10⁹⁢(97-digit number)
28253088908599393461…57480303688841625599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.650 Γ— 10⁹⁢(97-digit number)
56506177817198786922…14960607377683251199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.130 Γ— 10⁹⁷(98-digit number)
11301235563439757384…29921214755366502399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.260 Γ— 10⁹⁷(98-digit number)
22602471126879514769…59842429510733004799
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:57,611,909 XPMΒ·at block #6,795,976 Β· updates every 60s
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