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Block #2,124,548

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/19/2017, 11:53:22 PM Β· Difficulty 10.9181 Β· 4,716,916 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
adfe774c309949f8d6f574ae0d45e2d6662e4bf16d60eb397e10d7ffa15e9863
View on Chainz β†—

Height

#2,124,548

Difficulty

10.918057

Transactions

1

Size

242 B

Version

2

Bits

0aeb05ce

Nonce

1,456,106,460

Timestamp

5/19/2017, 11:53:22 PM

Confirmations

4,716,916

Mined by

⛏️ P2SHAMMJ7Ku9ctFmjCbBPtKsnh34K5ZYGbYo5z

Merkle Root

c003f4fceb53415bb43f0d11bd882deccb863fdf1d88b15ef435ed141c7877be
Transactions (1)
Coinbasec003f4fceb5341…35ed141c7877be
1 in β†’ 2 out8.3800 XPM152 B
AMMJ7Ku9…ZYGbYo5zAXbk7f7A…Tx7JECPG
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.

6.880 Γ— 10⁹⁡(96-digit number)
68806298919953099815…67302102905175073281
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
6.880 Γ— 10⁹⁡(96-digit number)
68806298919953099815…67302102905175073281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.376 Γ— 10⁹⁢(97-digit number)
13761259783990619963…34604205810350146561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.752 Γ— 10⁹⁢(97-digit number)
27522519567981239926…69208411620700293121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.504 Γ— 10⁹⁢(97-digit number)
55045039135962479852…38416823241400586241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.100 Γ— 10⁹⁷(98-digit number)
11009007827192495970…76833646482801172481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.201 Γ— 10⁹⁷(98-digit number)
22018015654384991940…53667292965602344961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.403 Γ— 10⁹⁷(98-digit number)
44036031308769983881…07334585931204689921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.807 Γ— 10⁹⁷(98-digit number)
88072062617539967763…14669171862409379841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.761 Γ— 10⁹⁸(99-digit number)
17614412523507993552…29338343724818759681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.522 Γ— 10⁹⁸(99-digit number)
35228825047015987105…58676687449637519361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.045 Γ— 10⁹⁸(99-digit number)
70457650094031974210…17353374899275038721
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:57,976,085 XPMΒ·at block #6,841,463 Β· updates every 60s
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