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Block #32,937

1CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/14/2013, 3:51:31 AM Β· Difficulty 7.9912 Β· 6,793,820 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
743967008b12b39d04f098ba94a9a18d5d5e6ae04a755b5ec6d98ecdbbc60b69
View on Chainz β†—

Height

#32,937

Difficulty

7.991185

Transactions

1

Size

200 B

Version

2

Bits

07fdbe45

Nonce

1,070

Timestamp

7/14/2013, 3:51:31 AM

Confirmations

6,793,820

Mined by

⛏️ P2SHASbRxSSzrfffuPGcuJ6s3bNYQdH5rkdjdH

Merkle Root

97430e4234e7f8a1f2fa0885a1a3dd9dfbc5b1a4da53fd0bf7295386abfa9b03
Transactions (1)
Coinbase97430e4234e7f8…295386abfa9b03
1 in β†’ 1 out15.6400 XPM109 B
ASbRxSSz…H5rkdjdH
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.

3.936 Γ— 10⁹⁢(97-digit number)
39361719693948472553…34456585080092133749
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
3.936 Γ— 10⁹⁢(97-digit number)
39361719693948472553…34456585080092133749
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.872 Γ— 10⁹⁢(97-digit number)
78723439387896945106…68913170160184267499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.574 Γ— 10⁹⁷(98-digit number)
15744687877579389021…37826340320368534999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.148 Γ— 10⁹⁷(98-digit number)
31489375755158778042…75652680640737069999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.297 Γ— 10⁹⁷(98-digit number)
62978751510317556085…51305361281474139999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.259 Γ— 10⁹⁸(99-digit number)
12595750302063511217…02610722562948279999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.519 Γ— 10⁹⁸(99-digit number)
25191500604127022434…05221445125896559999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,858,214 XPMΒ·at block #6,826,756 Β· updates every 60s
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