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Block #152,881

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/6/2013, 3:10:49 PM Β· Difficulty 9.8629 Β· 6,642,016 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7ca6539184f35215f976b87915b728a6a406bdcdb481227a7398cb9d895c4138
View on Chainz β†—

Height

#152,881

Difficulty

9.862927

Transactions

1

Size

200 B

Version

2

Bits

09dce8ce

Nonce

33,559,194

Timestamp

9/6/2013, 3:10:49 PM

Confirmations

6,642,016

Mined by

⛏️ P2SHAT5A2KL6kAm5Pa3anhC8W4LVscCT16n6i2

Merkle Root

231d83be69e30496c0202bb0a80454fd68e2e94b8e156de1191f31171f1ba100
Transactions (1)
Coinbase231d83be69e304…1f31171f1ba100
1 in β†’ 1 out10.2600 XPM112 B
AT5A2KL6…CT16n6i2
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.

8.261 Γ— 10⁸⁹(90-digit number)
82618103605983016012…15206636483542196279
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
8.261 Γ— 10⁸⁹(90-digit number)
82618103605983016012…15206636483542196279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.652 Γ— 10⁹⁰(91-digit number)
16523620721196603202…30413272967084392559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.304 Γ— 10⁹⁰(91-digit number)
33047241442393206405…60826545934168785119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.609 Γ— 10⁹⁰(91-digit number)
66094482884786412810…21653091868337570239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.321 Γ— 10⁹¹(92-digit number)
13218896576957282562…43306183736675140479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.643 Γ— 10⁹¹(92-digit number)
26437793153914565124…86612367473350280959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.287 Γ— 10⁹¹(92-digit number)
52875586307829130248…73224734946700561919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.057 Γ— 10⁹²(93-digit number)
10575117261565826049…46449469893401123839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.115 Γ— 10⁹²(93-digit number)
21150234523131652099…92898939786802247679
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:57,603,213 XPMΒ·at block #6,794,896 Β· updates every 60s
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