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Block #53,156

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/16/2013, 1:54:40 PM Β· Difficulty 8.9205 Β· 6,753,980 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
825070895d1035def3b2919013981ce8f730067a572d6c5b5c3416dc6d636fd2
View on Chainz β†—

Height

#53,156

Difficulty

8.920503

Transactions

1

Size

204 B

Version

2

Bits

08eba619

Nonce

136

Timestamp

7/16/2013, 1:54:40 PM

Confirmations

6,753,980

Mined by

⛏️ P2SHAbbkrW7G3d4gNVvA1rwosSVijDhVGWJss1

Merkle Root

6e7e247112aa779f2793745cc62e682d66841d84c5ceb8fe8947bcdb5c258229
Transactions (1)
Coinbase6e7e247112aa77…47bcdb5c258229
1 in β†’ 1 out12.5500 XPM110 B
AbbkrW7G…hVGWJss1
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.

1.579 Γ— 10¹⁰⁡(106-digit number)
15791959015751711001…10338271321889081119
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
1.579 Γ— 10¹⁰⁡(106-digit number)
15791959015751711001…10338271321889081119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.158 Γ— 10¹⁰⁡(106-digit number)
31583918031503422003…20676542643778162239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.316 Γ— 10¹⁰⁡(106-digit number)
63167836063006844007…41353085287556324479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.263 Γ— 10¹⁰⁢(107-digit number)
12633567212601368801…82706170575112648959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.526 Γ— 10¹⁰⁢(107-digit number)
25267134425202737602…65412341150225297919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.053 Γ— 10¹⁰⁢(107-digit number)
50534268850405475205…30824682300450595839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.010 Γ— 10¹⁰⁷(108-digit number)
10106853770081095041…61649364600901191679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.021 Γ— 10¹⁰⁷(108-digit number)
20213707540162190082…23298729201802383359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,701,193 XPMΒ·at block #6,807,135 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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