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Block #157,215

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/9/2013, 11:52:25 AM Β· Difficulty 9.8687 Β· 6,652,192 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a5f5fe15653e1766ff034e9bb9265cb7a1162f5dc554e393f2f6a5f82aeaf25f
View on Chainz β†—

Height

#157,215

Difficulty

9.868716

Transactions

1

Size

198 B

Version

2

Bits

09de642f

Nonce

191,688

Timestamp

9/9/2013, 11:52:25 AM

Confirmations

6,652,192

Mined by

⛏️ P2SHATr36r6GPrDWuY8aErt6RmRFsBKgmGvw5f

Merkle Root

1fe6da079b4c634e82d7086c52b0d0749583f9e5ebc7ec368fdbfcdcf015b46e
Transactions (1)
Coinbase1fe6da079b4c63…dbfcdcf015b46e
1 in β†’ 1 out10.2500 XPM109 B
ATr36r6G…KgmGvw5f
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.

2.603 Γ— 10⁹²(93-digit number)
26039186562682647097…18120636088706811279
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
2.603 Γ— 10⁹²(93-digit number)
26039186562682647097…18120636088706811279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.207 Γ— 10⁹²(93-digit number)
52078373125365294194…36241272177413622559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.041 Γ— 10⁹³(94-digit number)
10415674625073058838…72482544354827245119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.083 Γ— 10⁹³(94-digit number)
20831349250146117677…44965088709654490239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.166 Γ— 10⁹³(94-digit number)
41662698500292235355…89930177419308980479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.332 Γ— 10⁹³(94-digit number)
83325397000584470711…79860354838617960959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.666 Γ— 10⁹⁴(95-digit number)
16665079400116894142…59720709677235921919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.333 Γ— 10⁹⁴(95-digit number)
33330158800233788284…19441419354471843839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.666 Γ— 10⁹⁴(95-digit number)
66660317600467576568…38882838708943687679
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:57,719,331 XPMΒ·at block #6,809,406 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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