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Block #268,315

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/22/2013, 12:57:46 AM Β· Difficulty 9.9574 Β· 6,526,101 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
51de502196110c995b4207623e0c1994ef96bb95a52fa659a85234186d070833
View on Chainz β†—

Height

#268,315

Difficulty

9.957367

Transactions

1

Size

208 B

Version

2

Bits

09f515fd

Nonce

83,887,971

Timestamp

11/22/2013, 12:57:46 AM

Confirmations

6,526,101

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

bde36e3ad5f48773db5242a293f40661bf17ff1c54bce54eabe145236e71e6e9
Transactions (1)
Coinbasebde36e3ad5f487…e145236e71e6e9
1 in β†’ 1 out10.0700 XPM116 B
AcLBm5Z9…S683d7c3
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.

3.192 Γ— 10⁹⁹(100-digit number)
31925724887386952021…30183001210765803519
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
3.192 Γ— 10⁹⁹(100-digit number)
31925724887386952021…30183001210765803519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.385 Γ— 10⁹⁹(100-digit number)
63851449774773904042…60366002421531607039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.277 Γ— 10¹⁰⁰(101-digit number)
12770289954954780808…20732004843063214079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.554 Γ— 10¹⁰⁰(101-digit number)
25540579909909561616…41464009686126428159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.108 Γ— 10¹⁰⁰(101-digit number)
51081159819819123233…82928019372252856319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.021 Γ— 10¹⁰¹(102-digit number)
10216231963963824646…65856038744505712639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.043 Γ— 10¹⁰¹(102-digit number)
20432463927927649293…31712077489011425279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.086 Γ— 10¹⁰¹(102-digit number)
40864927855855298587…63424154978022850559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.172 Γ— 10¹⁰¹(102-digit number)
81729855711710597174…26848309956045701119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.634 Γ— 10¹⁰²(103-digit number)
16345971142342119434…53696619912091402239
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,599,362 XPMΒ·at block #6,794,415 Β· updates every 60s
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