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Block #2,171,396

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/22/2017, 1:59:11 AM Β· Difficulty 10.9054 Β· 4,669,710 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bfef906a50dd3b20d7f095202b2fe59a2dab160765d97291d9a3b2e43fe191a1
View on Chainz β†—

Height

#2,171,396

Difficulty

10.905422

Transactions

2

Size

425 B

Version

2

Bits

0ae7c9b5

Nonce

1,961,377,120

Timestamp

6/22/2017, 1:59:11 AM

Confirmations

4,669,710

Mined by

⛏️ P2SHAYv1e4ZxScucFnBXquVEq3o4Me5YZB1Z87

Merkle Root

d1f7ac45128cae748cef082c8d057cf82f9dac51ebb9ace6532fa5e209c15c29
Transactions (2)
Coinbasee3d6a79209a3c8…3b0b8676fcf82e
1 in β†’ 1 out8.4100 XPM110 B
AYv1e4Zx…5YZB1Z87
6332f77c332254…60908193f45814
1 in β†’ 2 out3.9900 XPM225 B
AUh6zJjq…yMn5wt6UAREGcr3m…ZEbfs93i
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.

8.044 Γ— 10⁹⁴(95-digit number)
80449369550434012438…08721071080674875121
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
8.044 Γ— 10⁹⁴(95-digit number)
80449369550434012438…08721071080674875121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.608 Γ— 10⁹⁡(96-digit number)
16089873910086802487…17442142161349750241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.217 Γ— 10⁹⁡(96-digit number)
32179747820173604975…34884284322699500481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.435 Γ— 10⁹⁡(96-digit number)
64359495640347209950…69768568645399000961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.287 Γ— 10⁹⁢(97-digit number)
12871899128069441990…39537137290798001921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.574 Γ— 10⁹⁢(97-digit number)
25743798256138883980…79074274581596003841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.148 Γ— 10⁹⁢(97-digit number)
51487596512277767960…58148549163192007681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.029 Γ— 10⁹⁷(98-digit number)
10297519302455553592…16297098326384015361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.059 Γ— 10⁹⁷(98-digit number)
20595038604911107184…32594196652768030721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.119 Γ— 10⁹⁷(98-digit number)
41190077209822214368…65188393305536061441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.238 Γ— 10⁹⁷(98-digit number)
82380154419644428736…30376786611072122881
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:57,973,213 XPMΒ·at block #6,841,105 Β· updates every 60s
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