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Block #2,877,453

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/12/2018, 1:53:23 AM Β· Difficulty 11.6484 Β· 3,964,082 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2a98a2db014c79a1c15e976c3be2e6df748052b939bb2881e786d40bd1acb0d2
View on Chainz β†—

Height

#2,877,453

Difficulty

11.648402

Transactions

1

Size

200 B

Version

2

Bits

0ba5fdb2

Nonce

76,137,926

Timestamp

10/12/2018, 1:53:23 AM

Confirmations

3,964,082

Mined by

⛏️ P2SHAYrQ2Qu1chGTHzKGRXKWu9iJ9MhqfF4fYg

Merkle Root

e62ffd4e2d02ed27372aee5c0bbabf48ece6d662fd2c85c70dfec5bd81ecee60
Transactions (1)
Coinbasee62ffd4e2d02ed…fec5bd81ecee60
1 in β†’ 1 out7.3600 XPM110 B
AYrQ2Qu1…hqfF4fYg
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.

8.493 Γ— 10⁹⁴(95-digit number)
84936798675366600650…64523966779777859201
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
8.493 Γ— 10⁹⁴(95-digit number)
84936798675366600650…64523966779777859201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.698 Γ— 10⁹⁡(96-digit number)
16987359735073320130…29047933559555718401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.397 Γ— 10⁹⁡(96-digit number)
33974719470146640260…58095867119111436801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.794 Γ— 10⁹⁡(96-digit number)
67949438940293280520…16191734238222873601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.358 Γ— 10⁹⁢(97-digit number)
13589887788058656104…32383468476445747201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.717 Γ— 10⁹⁢(97-digit number)
27179775576117312208…64766936952891494401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.435 Γ— 10⁹⁢(97-digit number)
54359551152234624416…29533873905782988801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.087 Γ— 10⁹⁷(98-digit number)
10871910230446924883…59067747811565977601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.174 Γ— 10⁹⁷(98-digit number)
21743820460893849766…18135495623131955201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.348 Γ— 10⁹⁷(98-digit number)
43487640921787699533…36270991246263910401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.697 Γ— 10⁹⁷(98-digit number)
86975281843575399066…72541982492527820801
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:57,976,663 XPMΒ·at block #6,841,534 Β· updates every 60s
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