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Block #25,937

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2013, 3:46:30 AM Β· Difficulty 7.9731 Β· 6,770,497 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e21d63b58e911811c6b04fa9219340792119ffca97d28ccee29c357bceebde5c
View on Chainz β†—

Height

#25,937

Difficulty

7.973080

Transactions

1

Size

200 B

Version

2

Bits

07f91bc4

Nonce

307

Timestamp

7/13/2013, 3:46:30 AM

Confirmations

6,770,497

Mined by

⛏️ P2SHATe6w9FhsmKSRYGqmeMzeBD3d2JApxuRga

Merkle Root

35c2187a53956deed340a0feb9b809e851276e5bf6dc88f678601977b8487b69
Transactions (1)
Coinbase35c2187a53956d…601977b8487b69
1 in β†’ 1 out15.7100 XPM108 B
ATe6w9Fh…JApxuRga
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.

9.194 Γ— 10⁹⁸(99-digit number)
91947971222467758778…83864330505330557279
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
9.194 Γ— 10⁹⁸(99-digit number)
91947971222467758778…83864330505330557279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.838 Γ— 10⁹⁹(100-digit number)
18389594244493551755…67728661010661114559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.677 Γ— 10⁹⁹(100-digit number)
36779188488987103511…35457322021322229119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.355 Γ— 10⁹⁹(100-digit number)
73558376977974207022…70914644042644458239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.471 Γ— 10¹⁰⁰(101-digit number)
14711675395594841404…41829288085288916479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.942 Γ— 10¹⁰⁰(101-digit number)
29423350791189682808…83658576170577832959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.884 Γ— 10¹⁰⁰(101-digit number)
58846701582379365617…67317152341155665919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.176 Γ— 10¹⁰¹(102-digit number)
11769340316475873123…34634304682311331839
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:57,615,464 XPMΒ·at block #6,796,433 Β· updates every 60s
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