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Block #2,729,241

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/1/2018, 7:16:54 AM Β· Difficulty 11.6272 Β· 4,104,493 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
89c69506c1935dd06119b0f085f1e8e09c7239d0505c68bf56020ca53d058df4
View on Chainz β†—

Height

#2,729,241

Difficulty

11.627214

Transactions

2

Size

69.75 KB

Version

2

Bits

0ba09111

Nonce

1,577,275,975

Timestamp

7/1/2018, 7:16:54 AM

Confirmations

4,104,493

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

f64afd1caa5f9e96c0acc952dea2b743fe8dcc50e59affad877341525efc6c3f
Transactions (2)
Coinbase24c2ab65dbc707…a9ee23303bbe80
1 in β†’ 1 out8.1000 XPM110 B
AZtxQr2F…7grUWrUz
e7da03b3a8fbbd…df4f419b1633e6
481 in β†’ 1 out28542.6818 XPM69.55 KB
ALPF8J52…Hjw4BMsG
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.

5.530 Γ— 10⁹⁡(96-digit number)
55305441722025669017…76249570934083580159
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
5.530 Γ— 10⁹⁡(96-digit number)
55305441722025669017…76249570934083580159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.106 Γ— 10⁹⁢(97-digit number)
11061088344405133803…52499141868167160319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.212 Γ— 10⁹⁢(97-digit number)
22122176688810267606…04998283736334320639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.424 Γ— 10⁹⁢(97-digit number)
44244353377620535213…09996567472668641279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.848 Γ— 10⁹⁢(97-digit number)
88488706755241070427…19993134945337282559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.769 Γ— 10⁹⁷(98-digit number)
17697741351048214085…39986269890674565119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.539 Γ— 10⁹⁷(98-digit number)
35395482702096428171…79972539781349130239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.079 Γ— 10⁹⁷(98-digit number)
70790965404192856342…59945079562698260479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.415 Γ— 10⁹⁸(99-digit number)
14158193080838571268…19890159125396520959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.831 Γ— 10⁹⁸(99-digit number)
28316386161677142536…39780318250793041919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.663 Γ— 10⁹⁸(99-digit number)
56632772323354285073…79560636501586083839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,914,096 XPMΒ·at block #6,833,733 Β· updates every 60s
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