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Block #3,226,119

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/15/2019, 8:53:29 AM Β· Difficulty 11.0045 Β· 3,613,613 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5b50c8d359141dbd390db3bcb2c0a09758a1623ef6e8b652b7cf8113ecb24b57
View on Chainz β†—

Height

#3,226,119

Difficulty

11.004489

Transactions

2

Size

869 B

Version

2

Bits

0b012634

Nonce

38,718,382

Timestamp

6/15/2019, 8:53:29 AM

Confirmations

3,613,613

Mined by

⛏️ P2SHARbm48qRsZyALB7gqdgsMMKGGA9xQc8DBX

Merkle Root

20571b398ed8795d23b8c82dd91e051c4c59fc05658536b5c4c5776d53c020c5
Transactions (2)
Coinbase5ed41bbef3baf3…5407a544fc0931
1 in β†’ 1 out8.2600 XPM110 B
ARbm48qR…9xQc8DBX
dcb9e135ce9ba4…87afcb05aef068
4 in β†’ 2 out247.7011 XPM669 B
AcAj4XgW…qv4FhTJGAZQgL5kt…6NE43uZs
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.

1.226 Γ— 10⁹⁡(96-digit number)
12267856289357991628…35757695536890082561
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
1.226 Γ— 10⁹⁡(96-digit number)
12267856289357991628…35757695536890082561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.453 Γ— 10⁹⁡(96-digit number)
24535712578715983257…71515391073780165121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.907 Γ— 10⁹⁡(96-digit number)
49071425157431966514…43030782147560330241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.814 Γ— 10⁹⁡(96-digit number)
98142850314863933028…86061564295120660481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.962 Γ— 10⁹⁢(97-digit number)
19628570062972786605…72123128590241320961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.925 Γ— 10⁹⁢(97-digit number)
39257140125945573211…44246257180482641921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.851 Γ— 10⁹⁢(97-digit number)
78514280251891146423…88492514360965283841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.570 Γ— 10⁹⁷(98-digit number)
15702856050378229284…76985028721930567681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.140 Γ— 10⁹⁷(98-digit number)
31405712100756458569…53970057443861135361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.281 Γ— 10⁹⁷(98-digit number)
62811424201512917138…07940114887722270721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.256 Γ— 10⁹⁸(99-digit number)
12562284840302583427…15880229775444541441
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:57,962,141 XPMΒ·at block #6,839,731 Β· updates every 60s
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