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Block #272,942

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/25/2013, 1:20:01 PM Β· Difficulty 9.9537 Β· 6,541,896 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1901001c822a2d01af7a29d799ca4d5fd4176572296da733fa56b6e7cb1a6665
View on Chainz β†—

Height

#272,942

Difficulty

9.953681

Transactions

2

Size

67.92 KB

Version

2

Bits

09f42468

Nonce

50,675

Timestamp

11/25/2013, 1:20:01 PM

Confirmations

6,541,896

Mined by

⛏️ P2SHAK8vfv36M7brWsuchmsSQ1sb2AhtyxfizB

Merkle Root

e499cdeec7c5f00a4c65380070cf679fd93c513c80b83be7736a1bb1fd17d234
Transactions (2)
Coinbase8a8274dc2d4a9f…8463019e90d455
1 in β†’ 1 out10.7800 XPM109 B
AK8vfv36…htyxfizB
a7a3ffab7ed742…61af0fd20f042a
468 in β†’ 2 out10.0100 XPM67.73 KB
AH5UMhMN…Vs3PwKK8ATn2ymL3…geaw6t52
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.

1.012 Γ— 10⁹⁡(96-digit number)
10121869888715217837…87526974502802472961
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
1.012 Γ— 10⁹⁡(96-digit number)
10121869888715217837…87526974502802472961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.024 Γ— 10⁹⁡(96-digit number)
20243739777430435674…75053949005604945921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.048 Γ— 10⁹⁡(96-digit number)
40487479554860871348…50107898011209891841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.097 Γ— 10⁹⁡(96-digit number)
80974959109721742696…00215796022419783681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.619 Γ— 10⁹⁢(97-digit number)
16194991821944348539…00431592044839567361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.238 Γ— 10⁹⁢(97-digit number)
32389983643888697078…00863184089679134721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.477 Γ— 10⁹⁢(97-digit number)
64779967287777394157…01726368179358269441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.295 Γ— 10⁹⁷(98-digit number)
12955993457555478831…03452736358716538881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.591 Γ— 10⁹⁷(98-digit number)
25911986915110957663…06905472717433077761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.182 Γ— 10⁹⁷(98-digit number)
51823973830221915326…13810945434866155521
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:57,762,787 XPMΒ·at block #6,814,837 Β· updates every 60s
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