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Block #2,297,767

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/16/2017, 3:42:14 AM Β· Difficulty 10.9458 Β· 4,517,095 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0469a23946b8150923d31730d0ed99c0bacc174711bd7c4109f56a5f1f79039c
View on Chainz β†—

Height

#2,297,767

Difficulty

10.945770

Transactions

2

Size

1.14 KB

Version

2

Bits

0af21e02

Nonce

986,670,444

Timestamp

9/16/2017, 3:42:14 AM

Confirmations

4,517,095

Mined by

⛏️ P2SHARVGHFUkzZiHAN4o58uQPap4xe3joD9UV6

Merkle Root

c2d25758fe2b5f011a732887deb0e199069557a80cd6f3f56f06d02917b542ca
Transactions (2)
Coinbase27799df207ccae…8534fd9700e74d
1 in β†’ 1 out8.3400 XPM109 B
ARVGHFUk…3joD9UV6
3466f1b88f97b5…62d1ab004f6826
6 in β†’ 2 out4500.0002 XPM966 B
AcxhUhX6…N8N8w2tmAPKYNw1b…CtyWwbJm
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.

1.161 Γ— 10⁹⁡(96-digit number)
11615652924153903557…74083640092198172161
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
1.161 Γ— 10⁹⁡(96-digit number)
11615652924153903557…74083640092198172161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.323 Γ— 10⁹⁡(96-digit number)
23231305848307807115…48167280184396344321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.646 Γ— 10⁹⁡(96-digit number)
46462611696615614230…96334560368792688641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.292 Γ— 10⁹⁡(96-digit number)
92925223393231228460…92669120737585377281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.858 Γ— 10⁹⁢(97-digit number)
18585044678646245692…85338241475170754561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.717 Γ— 10⁹⁢(97-digit number)
37170089357292491384…70676482950341509121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.434 Γ— 10⁹⁢(97-digit number)
74340178714584982768…41352965900683018241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.486 Γ— 10⁹⁷(98-digit number)
14868035742916996553…82705931801366036481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.973 Γ— 10⁹⁷(98-digit number)
29736071485833993107…65411863602732072961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.947 Γ— 10⁹⁷(98-digit number)
59472142971667986214…30823727205464145921
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:57,762,980 XPMΒ·at block #6,814,861 Β· updates every 60s
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