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Block #297,251

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/6/2013, 12:22:06 PM Β· Difficulty 9.9919 Β· 6,512,823 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4ffd436cea6372f6a449e598ba264b9cb63d245cd9d0d98dcb66e9b2b4117cde
View on Chainz β†—

Height

#297,251

Difficulty

9.991904

Transactions

1

Size

1.14 KB

Version

2

Bits

09fded74

Nonce

156,766

Timestamp

12/6/2013, 12:22:06 PM

Confirmations

6,512,823

Mined by

⛏️ #aRARzXge7STrHg8ZTMRW57MCNAWRCEjL5oYm

Merkle Root

bf2e317286ba14652ff84269ee9e84783564cbc12ac3210598269ccf751cbaa5
Transactions (1)
Coinbasebf2e317286ba14…269ccf751cbaa5
1 in β†’ 30 out9.9800 XPM1.06 KB
ARzXge7S…CEjL5oYmAZ2pPuKg…95SN2Yr7AKEwr54i…9BfmMkRhAQyr8Lw3…hs4nt3PnAaPASCNm…8mfBVejh
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.

5.502 Γ— 10⁹⁡(96-digit number)
55028150636551894485…52768443588050718721
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
5.502 Γ— 10⁹⁡(96-digit number)
55028150636551894485…52768443588050718721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.100 Γ— 10⁹⁢(97-digit number)
11005630127310378897…05536887176101437441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.201 Γ— 10⁹⁢(97-digit number)
22011260254620757794…11073774352202874881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.402 Γ— 10⁹⁢(97-digit number)
44022520509241515588…22147548704405749761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.804 Γ— 10⁹⁢(97-digit number)
88045041018483031176…44295097408811499521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.760 Γ— 10⁹⁷(98-digit number)
17609008203696606235…88590194817622999041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.521 Γ— 10⁹⁷(98-digit number)
35218016407393212470…77180389635245998081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.043 Γ— 10⁹⁷(98-digit number)
70436032814786424941…54360779270491996161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.408 Γ— 10⁹⁸(99-digit number)
14087206562957284988…08721558540983992321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.817 Γ— 10⁹⁸(99-digit number)
28174413125914569976…17443117081967984641
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:57,724,663 XPMΒ·at block #6,810,073 Β· updates every 60s
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