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Block #249,956

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/8/2013, 6:17:51 AM Β· Difficulty 9.9675 Β· 6,577,349 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8b5a817e5d9c7bb94af1eb6db74051c5e880340af948746a252d07296e4f14dd
View on Chainz β†—

Height

#249,956

Difficulty

9.967519

Transactions

1

Size

198 B

Version

2

Bits

09f7af55

Nonce

83,584

Timestamp

11/8/2013, 6:17:51 AM

Confirmations

6,577,349

Mined by

⛏️ P2SHARizkoMUwyJtecFyzbvPT4y2ms4dc14t9q

Merkle Root

3bde7fdb11b3108b391413012abadf47a0f98a4d66456ef1b20bb133acfa9ec4
Transactions (1)
Coinbase3bde7fdb11b310…0bb133acfa9ec4
1 in β†’ 1 out10.0500 XPM109 B
ARizkoMU…4dc14t9q
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.

1.537 Γ— 10⁹³(94-digit number)
15375329070901981627…49223849034959658201
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
1.537 Γ— 10⁹³(94-digit number)
15375329070901981627…49223849034959658201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.075 Γ— 10⁹³(94-digit number)
30750658141803963254…98447698069919316401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.150 Γ— 10⁹³(94-digit number)
61501316283607926508…96895396139838632801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.230 Γ— 10⁹⁴(95-digit number)
12300263256721585301…93790792279677265601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.460 Γ— 10⁹⁴(95-digit number)
24600526513443170603…87581584559354531201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.920 Γ— 10⁹⁴(95-digit number)
49201053026886341206…75163169118709062401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.840 Γ— 10⁹⁴(95-digit number)
98402106053772682413…50326338237418124801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.968 Γ— 10⁹⁡(96-digit number)
19680421210754536482…00652676474836249601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.936 Γ— 10⁹⁡(96-digit number)
39360842421509072965…01305352949672499201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.872 Γ— 10⁹⁡(96-digit number)
78721684843018145931…02610705899344998401
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:57,862,551 XPMΒ·at block #6,827,304 Β· updates every 60s
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