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Block #2,169,157

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/20/2017, 6:11:20 PM Β· Difficulty 10.8989 Β· 4,676,223 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4be3ef450f10f9e3a8281ef0832b10a20c9415f2f024de1de9e929844d44a2bb
View on Chainz β†—

Height

#2,169,157

Difficulty

10.898924

Transactions

1

Size

199 B

Version

2

Bits

0ae61fe9

Nonce

577,880,649

Timestamp

6/20/2017, 6:11:20 PM

Confirmations

4,676,223

Mined by

⛏️ P2SHANkhgJPyysJZpvHeX3L9g3NEjv9Vad2Zwu

Merkle Root

edd38b0655ae5396427855cdfaa7d7766739443147f1861c2b0fac52f9563573
Transactions (1)
Coinbaseedd38b0655ae53…0fac52f9563573
1 in β†’ 1 out8.4100 XPM110 B
ANkhgJPy…9Vad2Zwu
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.

2.104 Γ— 10⁹³(94-digit number)
21044706267087942966…78778189086034385421
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
2.104 Γ— 10⁹³(94-digit number)
21044706267087942966…78778189086034385421
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.208 Γ— 10⁹³(94-digit number)
42089412534175885932…57556378172068770841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.417 Γ— 10⁹³(94-digit number)
84178825068351771864…15112756344137541681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.683 Γ— 10⁹⁴(95-digit number)
16835765013670354372…30225512688275083361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.367 Γ— 10⁹⁴(95-digit number)
33671530027340708745…60451025376550166721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.734 Γ— 10⁹⁴(95-digit number)
67343060054681417491…20902050753100333441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.346 Γ— 10⁹⁡(96-digit number)
13468612010936283498…41804101506200666881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.693 Γ— 10⁹⁡(96-digit number)
26937224021872566996…83608203012401333761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.387 Γ— 10⁹⁡(96-digit number)
53874448043745133993…67216406024802667521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.077 Γ— 10⁹⁢(97-digit number)
10774889608749026798…34432812049605335041
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:58,007,485 XPMΒ·at block #6,845,379 Β· updates every 60s
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