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Block #244,251

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/4/2013, 6:08:09 PM Β· Difficulty 9.9627 Β· 6,562,828 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2694e3dc36f86b8533462c1d95510f6596af3936ed7f734cb2025e3b8dace31e
View on Chainz β†—

Height

#244,251

Difficulty

9.962719

Transactions

1

Size

200 B

Version

2

Bits

09f674bf

Nonce

54,763

Timestamp

11/4/2013, 6:08:09 PM

Confirmations

6,562,828

Mined by

⛏️ P2SHAFv4GxfhFidL8Dd2giAFtoCmE3LfEWFx48

Merkle Root

91e693d54ba4ff1248a529ed8556895d6899c88fb5ced689b695734f4495598d
Transactions (1)
Coinbase91e693d54ba4ff…95734f4495598d
1 in β†’ 1 out10.0600 XPM109 B
AFv4Gxfh…LfEWFx48
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.

3.879 Γ— 10⁹⁢(97-digit number)
38792134581669719851…93829734397696967681
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
3.879 Γ— 10⁹⁢(97-digit number)
38792134581669719851…93829734397696967681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.758 Γ— 10⁹⁢(97-digit number)
77584269163339439702…87659468795393935361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.551 Γ— 10⁹⁷(98-digit number)
15516853832667887940…75318937590787870721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.103 Γ— 10⁹⁷(98-digit number)
31033707665335775881…50637875181575741441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.206 Γ— 10⁹⁷(98-digit number)
62067415330671551762…01275750363151482881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.241 Γ— 10⁹⁸(99-digit number)
12413483066134310352…02551500726302965761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.482 Γ— 10⁹⁸(99-digit number)
24826966132268620704…05103001452605931521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.965 Γ— 10⁹⁸(99-digit number)
49653932264537241409…10206002905211863041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.930 Γ— 10⁹⁸(99-digit number)
99307864529074482819…20412005810423726081
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:57,700,728 XPMΒ·at block #6,807,078 Β· updates every 60s
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