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Block #274,619

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/26/2013, 8:55:39 AM Β· Difficulty 9.9581 Β· 6,538,378 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
091a55ef1fe3abbb2a92b42715afdd25e9a630bbdad6afcd8ca83d00d123eded
View on Chainz β†—

Height

#274,619

Difficulty

9.958116

Transactions

1

Size

208 B

Version

2

Bits

09f5471a

Nonce

42,675

Timestamp

11/26/2013, 8:55:39 AM

Confirmations

6,538,378

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

130537d645f44f6cc45839627ed03870106a72d3b791d73f0d01d007ab0612b1
Transactions (1)
Coinbase130537d645f44f…01d007ab0612b1
1 in β†’ 1 out10.0700 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.

4.628 Γ— 10⁹⁸(99-digit number)
46289985407209558828…08420216200989749761
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
4.628 Γ— 10⁹⁸(99-digit number)
46289985407209558828…08420216200989749761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.257 Γ— 10⁹⁸(99-digit number)
92579970814419117656…16840432401979499521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.851 Γ— 10⁹⁹(100-digit number)
18515994162883823531…33680864803958999041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.703 Γ— 10⁹⁹(100-digit number)
37031988325767647062…67361729607917998081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.406 Γ— 10⁹⁹(100-digit number)
74063976651535294124…34723459215835996161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.481 Γ— 10¹⁰⁰(101-digit number)
14812795330307058824…69446918431671992321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.962 Γ— 10¹⁰⁰(101-digit number)
29625590660614117649…38893836863343984641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.925 Γ— 10¹⁰⁰(101-digit number)
59251181321228235299…77787673726687969281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.185 Γ— 10¹⁰¹(102-digit number)
11850236264245647059…55575347453375938561
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,748,016 XPMΒ·at block #6,812,996 Β· updates every 60s
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