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Block #2,935,918

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/23/2018, 3:16:23 PM Β· Difficulty 11.3880 Β· 3,907,000 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7e69bc294b504c2a264f7b180a5c85e9188a417a5d6f8f538d1371b593df0dce
View on Chainz β†—

Height

#2,935,918

Difficulty

11.387971

Transactions

1

Size

199 B

Version

2

Bits

0b63520d

Nonce

1,904,801,126

Timestamp

11/23/2018, 3:16:23 PM

Confirmations

3,907,000

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

98e62e7310336dd0882180846aa9c01c42255ce127e8c33471111218c452c91c
Transactions (1)
Coinbase98e62e7310336d…111218c452c91c
1 in β†’ 1 out7.7000 XPM109 B
AUhjokok…k5m93PZR
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.

4.487 Γ— 10⁹⁴(95-digit number)
44874204426169591940…26960258290321667151
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
4.487 Γ— 10⁹⁴(95-digit number)
44874204426169591940…26960258290321667151
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.974 Γ— 10⁹⁴(95-digit number)
89748408852339183880…53920516580643334301
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.794 Γ— 10⁹⁡(96-digit number)
17949681770467836776…07841033161286668601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.589 Γ— 10⁹⁡(96-digit number)
35899363540935673552…15682066322573337201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.179 Γ— 10⁹⁡(96-digit number)
71798727081871347104…31364132645146674401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.435 Γ— 10⁹⁢(97-digit number)
14359745416374269420…62728265290293348801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.871 Γ— 10⁹⁢(97-digit number)
28719490832748538841…25456530580586697601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.743 Γ— 10⁹⁢(97-digit number)
57438981665497077683…50913061161173395201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.148 Γ— 10⁹⁷(98-digit number)
11487796333099415536…01826122322346790401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.297 Γ— 10⁹⁷(98-digit number)
22975592666198831073…03652244644693580801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.595 Γ— 10⁹⁷(98-digit number)
45951185332397662146…07304489289387161601
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:57,987,691 XPMΒ·at block #6,842,917 Β· updates every 60s
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