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Block #2,877,048

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/11/2018, 6:44:58 PM Β· Difficulty 11.6500 Β· 3,967,840 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eb9b2cc5d8e878ed07d4931c97405f3584991b3215ce1982b2d66471eb75f269
View on Chainz β†—

Height

#2,877,048

Difficulty

11.649978

Transactions

1

Size

201 B

Version

2

Bits

0ba664fa

Nonce

481,135,065

Timestamp

10/11/2018, 6:44:58 PM

Confirmations

3,967,840

Mined by

⛏️ P2SHANb8RYBDfhjUaR3RLhMcde1YUHAqgwxndN

Merkle Root

ab584458f950dd1766af8ba00986efdfd8df914d45f9b3b5bbec5b4e16a017f3
Transactions (1)
Coinbaseab584458f950dd…ec5b4e16a017f3
1 in β†’ 1 out7.3600 XPM110 B
ANb8RYBD…AqgwxndN
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.

2.381 Γ— 10⁹⁷(98-digit number)
23812574337255505375…00633162835707811841
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
2.381 Γ— 10⁹⁷(98-digit number)
23812574337255505375…00633162835707811841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.762 Γ— 10⁹⁷(98-digit number)
47625148674511010751…01266325671415623681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.525 Γ— 10⁹⁷(98-digit number)
95250297349022021503…02532651342831247361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.905 Γ— 10⁹⁸(99-digit number)
19050059469804404300…05065302685662494721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.810 Γ— 10⁹⁸(99-digit number)
38100118939608808601…10130605371324989441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.620 Γ— 10⁹⁸(99-digit number)
76200237879217617202…20261210742649978881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.524 Γ— 10⁹⁹(100-digit number)
15240047575843523440…40522421485299957761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.048 Γ— 10⁹⁹(100-digit number)
30480095151687046881…81044842970599915521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.096 Γ— 10⁹⁹(100-digit number)
60960190303374093762…62089685941199831041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.219 Γ— 10¹⁰⁰(101-digit number)
12192038060674818752…24179371882399662081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.438 Γ— 10¹⁰⁰(101-digit number)
24384076121349637504…48358743764799324161
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:58,003,519 XPMΒ·at block #6,844,887 Β· updates every 60s
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