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Block #2,646,398

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2018, 8:26:45 AM Β· Difficulty 11.7494 Β· 4,186,143 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3b002bd4ced6a431d140d39a72eedb50f553404572f0ebeb9ada80d660413d00
View on Chainz β†—

Height

#2,646,398

Difficulty

11.749407

Transactions

1

Size

200 B

Version

2

Bits

0bbfd925

Nonce

916,179,096

Timestamp

5/3/2018, 8:26:45 AM

Confirmations

4,186,143

Mined by

⛏️ P2SHASdRRKwJQUYrMW3Qttm681yVWSFYPjkNpy

Merkle Root

c106418852c3b2774d7fac0b20d5eb198571cc4b121cadf33362f38ee3c5714c
Transactions (1)
Coinbasec106418852c3b2…62f38ee3c5714c
1 in β†’ 1 out7.2300 XPM110 B
ASdRRKwJ…FYPjkNpy
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.

1.644 Γ— 10⁹⁴(95-digit number)
16447699539301856628…31312051134671527761
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
1.644 Γ— 10⁹⁴(95-digit number)
16447699539301856628…31312051134671527761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.289 Γ— 10⁹⁴(95-digit number)
32895399078603713256…62624102269343055521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.579 Γ— 10⁹⁴(95-digit number)
65790798157207426513…25248204538686111041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.315 Γ— 10⁹⁡(96-digit number)
13158159631441485302…50496409077372222081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.631 Γ— 10⁹⁡(96-digit number)
26316319262882970605…00992818154744444161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.263 Γ— 10⁹⁡(96-digit number)
52632638525765941210…01985636309488888321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.052 Γ— 10⁹⁢(97-digit number)
10526527705153188242…03971272618977776641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.105 Γ— 10⁹⁢(97-digit number)
21053055410306376484…07942545237955553281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.210 Γ— 10⁹⁢(97-digit number)
42106110820612752968…15885090475911106561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.421 Γ— 10⁹⁢(97-digit number)
84212221641225505936…31770180951822213121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.684 Γ— 10⁹⁷(98-digit number)
16842444328245101187…63540361903644426241
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:57,904,490 XPMΒ·at block #6,832,540 Β· updates every 60s
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