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Block #33,238

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/14/2013, 4:28:45 AM Β· Difficulty 7.9916 Β· 6,762,450 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
01e5de9682a7b767fcc8404afc4afbe12f3f06d2c7188090e300e40ade155661
View on Chainz β†—

Height

#33,238

Difficulty

7.991643

Transactions

1

Size

199 B

Version

2

Bits

07fddc4e

Nonce

539

Timestamp

7/14/2013, 4:28:45 AM

Confirmations

6,762,450

Mined by

⛏️ P2SHAGemJXng9Py5jf5TzegELEhNUUw1K3MEut

Merkle Root

76d604e7c74a71ada5329602906cab17a6b2b945f899d524bcbe30c28f6b0a35
Transactions (1)
Coinbase76d604e7c74a71…be30c28f6b0a35
1 in β†’ 1 out15.6400 XPM109 B
AGemJXng…w1K3MEut
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.

1.223 Γ— 10⁹⁡(96-digit number)
12234860598579717456…13088389119981221749
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
1.223 Γ— 10⁹⁡(96-digit number)
12234860598579717456…13088389119981221749
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.446 Γ— 10⁹⁡(96-digit number)
24469721197159434913…26176778239962443499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.893 Γ— 10⁹⁡(96-digit number)
48939442394318869827…52353556479924886999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.787 Γ— 10⁹⁡(96-digit number)
97878884788637739654…04707112959849773999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.957 Γ— 10⁹⁢(97-digit number)
19575776957727547930…09414225919699547999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.915 Γ— 10⁹⁢(97-digit number)
39151553915455095861…18828451839399095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.830 Γ— 10⁹⁢(97-digit number)
78303107830910191723…37656903678798191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.566 Γ— 10⁹⁷(98-digit number)
15660621566182038344…75313807357596383999
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:57,609,573 XPMΒ·at block #6,795,687 Β· updates every 60s
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