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Block #254,901

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/10/2013, 11:38:06 PM Β· Difficulty 9.9736 Β· 6,559,035 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
454a8ee606316011f3d2dcb022f9356409106638c74b04c87c1a5f28c490aad0
View on Chainz β†—

Height

#254,901

Difficulty

9.973642

Transactions

1

Size

199 B

Version

2

Bits

09f94093

Nonce

2,797

Timestamp

11/10/2013, 11:38:06 PM

Confirmations

6,559,035

Mined by

⛏️ P2SHAZ4EMqbMPmp2SB7iQdjRrKaKVuWjnAzqk5

Merkle Root

ee1e5caa0f7e04e6035d73c2fca23c7264ab1bfc0491855c2cbea50e27073a2b
Transactions (1)
Coinbaseee1e5caa0f7e04…bea50e27073a2b
1 in β†’ 1 out10.0400 XPM109 B
AZ4EMqbM…WjnAzqk5
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.

8.390 Γ— 10⁹³(94-digit number)
83907983818698111026…61051511832008136021
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
8.390 Γ— 10⁹³(94-digit number)
83907983818698111026…61051511832008136021
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.678 Γ— 10⁹⁴(95-digit number)
16781596763739622205…22103023664016272041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.356 Γ— 10⁹⁴(95-digit number)
33563193527479244410…44206047328032544081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.712 Γ— 10⁹⁴(95-digit number)
67126387054958488821…88412094656065088161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.342 Γ— 10⁹⁡(96-digit number)
13425277410991697764…76824189312130176321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.685 Γ— 10⁹⁡(96-digit number)
26850554821983395528…53648378624260352641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.370 Γ— 10⁹⁡(96-digit number)
53701109643966791057…07296757248520705281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.074 Γ— 10⁹⁢(97-digit number)
10740221928793358211…14593514497041410561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.148 Γ— 10⁹⁢(97-digit number)
21480443857586716422…29187028994082821121
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:57,755,564 XPMΒ·at block #6,813,935 Β· updates every 60s
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