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Block #2,380,960

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/15/2017, 9:28:16 PM Β· Difficulty 10.8770 Β· 4,462,341 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5c696f4538500755e5b6c29463e8623e09227b440e488eec3824277ed596b860
View on Chainz β†—

Height

#2,380,960

Difficulty

10.877028

Transactions

2

Size

540 B

Version

2

Bits

0ae084e0

Nonce

672,110,711

Timestamp

11/15/2017, 9:28:16 PM

Confirmations

4,462,341

Mined by

⛏️ P2SHAdjuxcvNvYTpq6yH1Yn8WQm9mYxkZob4fZ

Merkle Root

f3a66c202f29a27bf530e58f8c4f957e52233b57cfad581d3b93de1c337c1e42
Transactions (2)
Coinbasee73e72bb7fba8c…6473cd2fa4074a
1 in β†’ 1 out8.4500 XPM110 B
AdjuxcvN…xkZob4fZ
2a1e5cbcd2cf6f…fce3c41aadfa83
2 in β†’ 1 out1.0940 XPM340 B
AZzRvmC3…nf4TxJDX
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.

8.300 Γ— 10⁹⁴(95-digit number)
83005813559770625813…04712186299690589759
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
8.300 Γ— 10⁹⁴(95-digit number)
83005813559770625813…04712186299690589759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.660 Γ— 10⁹⁡(96-digit number)
16601162711954125162…09424372599381179519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.320 Γ— 10⁹⁡(96-digit number)
33202325423908250325…18848745198762359039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.640 Γ— 10⁹⁡(96-digit number)
66404650847816500650…37697490397524718079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.328 Γ— 10⁹⁢(97-digit number)
13280930169563300130…75394980795049436159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.656 Γ— 10⁹⁢(97-digit number)
26561860339126600260…50789961590098872319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.312 Γ— 10⁹⁢(97-digit number)
53123720678253200520…01579923180197744639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.062 Γ— 10⁹⁷(98-digit number)
10624744135650640104…03159846360395489279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.124 Γ— 10⁹⁷(98-digit number)
21249488271301280208…06319692720790978559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.249 Γ— 10⁹⁷(98-digit number)
42498976542602560416…12639385441581957119
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:57,990,773 XPMΒ·at block #6,843,300 Β· updates every 60s
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