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Block #2,657,760

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/12/2018, 6:44:37 AM Β· Difficulty 11.6633 Β· 4,181,382 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
71c9ef0cb3758f32c808efd379aab22062182f9b72693962ec2cbae24e304b61
View on Chainz β†—

Height

#2,657,760

Difficulty

11.663346

Transactions

1

Size

200 B

Version

2

Bits

0ba9d105

Nonce

536,717,573

Timestamp

5/12/2018, 6:44:37 AM

Confirmations

4,181,382

Mined by

⛏️ P2SHAH6pqge5zSJ9pJz3zcktrK3HYsXenpm8wZ

Merkle Root

b8acafa38ab24324dc960d71ed4f131dbb4b62497c8771cecc2ac4dd2dbdab41
Transactions (1)
Coinbaseb8acafa38ab243…2ac4dd2dbdab41
1 in β†’ 1 out7.3400 XPM110 B
AH6pqge5…Xenpm8wZ
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.

1.466 Γ— 10⁹⁡(96-digit number)
14667459240099161380…61069755289866107201
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
1.466 Γ— 10⁹⁡(96-digit number)
14667459240099161380…61069755289866107201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.933 Γ— 10⁹⁡(96-digit number)
29334918480198322760…22139510579732214401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.866 Γ— 10⁹⁡(96-digit number)
58669836960396645521…44279021159464428801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.173 Γ— 10⁹⁢(97-digit number)
11733967392079329104…88558042318928857601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.346 Γ— 10⁹⁢(97-digit number)
23467934784158658208…77116084637857715201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.693 Γ— 10⁹⁢(97-digit number)
46935869568317316417…54232169275715430401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.387 Γ— 10⁹⁢(97-digit number)
93871739136634632834…08464338551430860801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.877 Γ— 10⁹⁷(98-digit number)
18774347827326926566…16928677102861721601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.754 Γ— 10⁹⁷(98-digit number)
37548695654653853133…33857354205723443201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.509 Γ— 10⁹⁷(98-digit number)
75097391309307706267…67714708411446886401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.501 Γ— 10⁹⁸(99-digit number)
15019478261861541253…35429416822893772801
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:57,957,415 XPMΒ·at block #6,839,141 Β· updates every 60s
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