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Block #2,703,224

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/13/2018, 5:04:15 AM Β· Difficulty 11.6289 Β· 4,109,593 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2af90db326b4e999e7fb4f34aa04c70684ee3d9c3a6296b55a1ebd2a004558e7
View on Chainz β†—

Height

#2,703,224

Difficulty

11.628943

Transactions

2

Size

723 B

Version

2

Bits

0ba10268

Nonce

615,024,699

Timestamp

6/13/2018, 5:04:15 AM

Confirmations

4,109,593

Mined by

⛏️ P2SHAZGrp1B4tycvKt2bn3DXRUqCoi4vqLXcrD

Merkle Root

a4f155dc36aeb03fd0b3ef5a21a3a0bd4fc58567765fac22307b33966711d4a5
Transactions (2)
Coinbased46716698402c3…6416eb66d0be58
1 in β†’ 1 out7.3900 XPM110 B
AZGrp1B4…4vqLXcrD
2d9d29ba5f0a94…310e15bb4d8f20
3 in β†’ 2 out12.1073 XPM522 B
AdepddBi…eU9B97ytAKkYdF1N…5Yz8MUXP
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.

1.159 Γ— 10⁹⁷(98-digit number)
11594466077741975223…63378250145289543681
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
1.159 Γ— 10⁹⁷(98-digit number)
11594466077741975223…63378250145289543681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.318 Γ— 10⁹⁷(98-digit number)
23188932155483950447…26756500290579087361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.637 Γ— 10⁹⁷(98-digit number)
46377864310967900895…53513000581158174721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.275 Γ— 10⁹⁷(98-digit number)
92755728621935801790…07026001162316349441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.855 Γ— 10⁹⁸(99-digit number)
18551145724387160358…14052002324632698881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.710 Γ— 10⁹⁸(99-digit number)
37102291448774320716…28104004649265397761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.420 Γ— 10⁹⁸(99-digit number)
74204582897548641432…56208009298530795521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.484 Γ— 10⁹⁹(100-digit number)
14840916579509728286…12416018597061591041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.968 Γ— 10⁹⁹(100-digit number)
29681833159019456572…24832037194123182081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.936 Γ— 10⁹⁹(100-digit number)
59363666318038913145…49664074388246364161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.187 Γ— 10¹⁰⁰(101-digit number)
11872733263607782629…99328148776492728321
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,746,582 XPMΒ·at block #6,812,816 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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