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Block #291,298

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/3/2013, 2:50:31 AM Β· Difficulty 9.9898 Β· 6,514,404 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a78e2e52be567ce702e112708db41062203f4272a17062f5f11cb5eed9dd2a78
View on Chainz β†—

Height

#291,298

Difficulty

9.989787

Transactions

2

Size

390 B

Version

2

Bits

09fd62af

Nonce

281,630

Timestamp

12/3/2013, 2:50:31 AM

Confirmations

6,514,404

Mined by

⛏️ P2SHAMDDjcKidTR7e5DmAbqsZdJTifMcrtk5gH

Merkle Root

55e1f462b7c7fd63151ab96d2a2e6b9236c355198944a23e4c45167c54e1fe73
Transactions (2)
Coinbase8a0fe4b439f899…6b1a251159ba66
1 in β†’ 1 out10.0200 XPM109 B
AMDDjcKi…Mcrtk5gH
c8de3c527e0a34…a008ec839ebd47
1 in β†’ 1 out14.2576 XPM192 B
ALNb65sp…wp28q4CY
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.

2.373 Γ— 10⁹³(94-digit number)
23734815066388633513…32398035588581539661
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
2.373 Γ— 10⁹³(94-digit number)
23734815066388633513…32398035588581539661
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.746 Γ— 10⁹³(94-digit number)
47469630132777267027…64796071177163079321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.493 Γ— 10⁹³(94-digit number)
94939260265554534054…29592142354326158641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.898 Γ— 10⁹⁴(95-digit number)
18987852053110906810…59184284708652317281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.797 Γ— 10⁹⁴(95-digit number)
37975704106221813621…18368569417304634561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.595 Γ— 10⁹⁴(95-digit number)
75951408212443627243…36737138834609269121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.519 Γ— 10⁹⁡(96-digit number)
15190281642488725448…73474277669218538241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.038 Γ— 10⁹⁡(96-digit number)
30380563284977450897…46948555338437076481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.076 Γ— 10⁹⁡(96-digit number)
60761126569954901795…93897110676874152961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.215 Γ— 10⁹⁢(97-digit number)
12152225313990980359…87794221353748305921
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:57,689,697 XPMΒ·at block #6,805,701 Β· updates every 60s
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