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Block #2,868,648

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/5/2018, 5:18:24 PM Β· Difficulty 11.6717 Β· 3,975,352 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
81973be1be1cbd40bc6b69ec6a6b8db0c40a7ebf5140e98851c5273c7a55ff6a
View on Chainz β†—

Height

#2,868,648

Difficulty

11.671656

Transactions

1

Size

200 B

Version

2

Bits

0babf1a2

Nonce

320,645,052

Timestamp

10/5/2018, 5:18:24 PM

Confirmations

3,975,352

Mined by

⛏️ P2SHALtWZAFsAXkz2GNeBd9JYYRod8TjnHwkqG

Merkle Root

ad3364b1298be367728bc99f849c7bd1283889c5b3ba803a99f2826f9789769f
Transactions (1)
Coinbasead3364b1298be3…f2826f9789769f
1 in β†’ 1 out7.3300 XPM109 B
ALtWZAFs…TjnHwkqG
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.

2.629 Γ— 10⁹⁷(98-digit number)
26291791181943408970…62247939061766840321
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.629 Γ— 10⁹⁷(98-digit number)
26291791181943408970…62247939061766840321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.258 Γ— 10⁹⁷(98-digit number)
52583582363886817940…24495878123533680641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.051 Γ— 10⁹⁸(99-digit number)
10516716472777363588…48991756247067361281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.103 Γ— 10⁹⁸(99-digit number)
21033432945554727176…97983512494134722561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.206 Γ— 10⁹⁸(99-digit number)
42066865891109454352…95967024988269445121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.413 Γ— 10⁹⁸(99-digit number)
84133731782218908704…91934049976538890241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.682 Γ— 10⁹⁹(100-digit number)
16826746356443781740…83868099953077780481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.365 Γ— 10⁹⁹(100-digit number)
33653492712887563481…67736199906155560961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.730 Γ— 10⁹⁹(100-digit number)
67306985425775126963…35472399812311121921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.346 Γ— 10¹⁰⁰(101-digit number)
13461397085155025392…70944799624622243841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.692 Γ— 10¹⁰⁰(101-digit number)
26922794170310050785…41889599249244487681
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,996,382 XPMΒ·at block #6,843,999 Β· updates every 60s
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