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Block #159,116

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2013, 9:25:07 PM Β· Difficulty 9.8659 Β· 6,648,034 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
94798064fbf5326f04713bf850899491dd66aabf50ef7bfbe5f11738598db52d
View on Chainz β†—

Height

#159,116

Difficulty

9.865894

Transactions

1

Size

199 B

Version

2

Bits

09ddab3a

Nonce

710,877

Timestamp

9/10/2013, 9:25:07 PM

Confirmations

6,648,034

Mined by

⛏️ P2SHAKhaGKFX4s17sd56QzVFtsa8mSKjeAXtBv

Merkle Root

8e4b0eba333574d28434ea9b4118a8aa96ab406752f322f23b403cb756ee52ff
Transactions (1)
Coinbase8e4b0eba333574…403cb756ee52ff
1 in β†’ 1 out10.2600 XPM109 B
AKhaGKFX…KjeAXtBv
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.

8.395 Γ— 10⁹⁡(96-digit number)
83955231253271828918…10812249521176827389
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
8.395 Γ— 10⁹⁡(96-digit number)
83955231253271828918…10812249521176827389
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.679 Γ— 10⁹⁢(97-digit number)
16791046250654365783…21624499042353654779
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.358 Γ— 10⁹⁢(97-digit number)
33582092501308731567…43248998084707309559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.716 Γ— 10⁹⁢(97-digit number)
67164185002617463134…86497996169414619119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.343 Γ— 10⁹⁷(98-digit number)
13432837000523492626…72995992338829238239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.686 Γ— 10⁹⁷(98-digit number)
26865674001046985253…45991984677658476479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.373 Γ— 10⁹⁷(98-digit number)
53731348002093970507…91983969355316952959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.074 Γ— 10⁹⁸(99-digit number)
10746269600418794101…83967938710633905919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.149 Γ— 10⁹⁸(99-digit number)
21492539200837588203…67935877421267811839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.298 Γ— 10⁹⁸(99-digit number)
42985078401675176406…35871754842535623679
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:57,701,206 XPMΒ·at block #6,807,149 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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