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Block #272,288

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/25/2013, 4:22:57 AM Β· Difficulty 9.9526 Β· 6,545,650 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e5f00fc425ae1c89bf36e09cc1ba9a2c01ece08094e48dbca4ed9ba49f552561
View on Chainz β†—

Height

#272,288

Difficulty

9.952580

Transactions

1

Size

207 B

Version

2

Bits

09f3dc45

Nonce

172,755

Timestamp

11/25/2013, 4:22:57 AM

Confirmations

6,545,650

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

02d679b2eaaa2545e2e05b1a21e5451c9e07d98328051aa8ee000f795c632d37
Transactions (1)
Coinbase02d679b2eaaa25…000f795c632d37
1 in β†’ 1 out10.0800 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.833 Γ— 10⁹⁢(97-digit number)
18331573141703796456…48458376702719866881
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
1.833 Γ— 10⁹⁢(97-digit number)
18331573141703796456…48458376702719866881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.666 Γ— 10⁹⁢(97-digit number)
36663146283407592912…96916753405439733761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.332 Γ— 10⁹⁢(97-digit number)
73326292566815185825…93833506810879467521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.466 Γ— 10⁹⁷(98-digit number)
14665258513363037165…87667013621758935041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.933 Γ— 10⁹⁷(98-digit number)
29330517026726074330…75334027243517870081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.866 Γ— 10⁹⁷(98-digit number)
58661034053452148660…50668054487035740161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.173 Γ— 10⁹⁸(99-digit number)
11732206810690429732…01336108974071480321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.346 Γ— 10⁹⁸(99-digit number)
23464413621380859464…02672217948142960641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.692 Γ— 10⁹⁸(99-digit number)
46928827242761718928…05344435896285921281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.385 Γ— 10⁹⁸(99-digit number)
93857654485523437857…10688871792571842561
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:57,787,569 XPMΒ·at block #6,817,937 Β· updates every 60s
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