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Block #1,231,727

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/11/2015, 11:47:00 AM Β· Difficulty 10.7402 Β· 5,573,436 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2ce69b65b9cdb05b3772dcb2ccd09fdb349f0e05b4a2a91df8c7b21f4c0fa4bd
View on Chainz β†—

Height

#1,231,727

Difficulty

10.740177

Transactions

1

Size

199 B

Version

2

Bits

0abd7c39

Nonce

697,781

Timestamp

9/11/2015, 11:47:00 AM

Confirmations

5,573,436

Mined by

⛏️ P2SHAdR3SMVt6VHfdqBhG6aGDPFuE82zrhAR7g

Merkle Root

d8415985545f790a1a871d4b503e052a1044d1121034a69ae17410536a5d38e5
Transactions (1)
Coinbased8415985545f79…7410536a5d38e5
1 in β†’ 1 out8.6600 XPM109 B
AdR3SMVt…2zrhAR7g
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.

2.264 Γ— 10⁹⁡(96-digit number)
22641458898553458528…44105828837412924399
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
2.264 Γ— 10⁹⁡(96-digit number)
22641458898553458528…44105828837412924399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.528 Γ— 10⁹⁡(96-digit number)
45282917797106917056…88211657674825848799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.056 Γ— 10⁹⁡(96-digit number)
90565835594213834113…76423315349651697599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.811 Γ— 10⁹⁢(97-digit number)
18113167118842766822…52846630699303395199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.622 Γ— 10⁹⁢(97-digit number)
36226334237685533645…05693261398606790399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.245 Γ— 10⁹⁢(97-digit number)
72452668475371067290…11386522797213580799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.449 Γ— 10⁹⁷(98-digit number)
14490533695074213458…22773045594427161599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.898 Γ— 10⁹⁷(98-digit number)
28981067390148426916…45546091188854323199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.796 Γ— 10⁹⁷(98-digit number)
57962134780296853832…91092182377708646399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.159 Γ— 10⁹⁸(99-digit number)
11592426956059370766…82184364755417292799
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:57,685,371 XPMΒ·at block #6,805,162 Β· updates every 60s
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