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Block #2,943,414

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/28/2018, 7:20:58 PM Β· Difficulty 11.3947 Β· 3,901,885 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a69cf7ddf4d3ed807b6396bca9321ccbeaf8e5e0bb2d55281be087525c5e6ef5
View on Chainz β†—

Height

#2,943,414

Difficulty

11.394718

Transactions

1

Size

199 B

Version

2

Bits

0b650c43

Nonce

1,773,806,687

Timestamp

11/28/2018, 7:20:58 PM

Confirmations

3,901,885

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

600195fc80e3f06d99f9c9e79efeee863db185ac4bef81e1b32031119f1518ae
Transactions (1)
Coinbase600195fc80e3f0…2031119f1518ae
1 in β†’ 1 out7.6900 XPM110 B
AbXwmGxD…4XXYP765
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.

2.480 Γ— 10⁹³(94-digit number)
24804964104639261435…06497960821931031971
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
2.480 Γ— 10⁹³(94-digit number)
24804964104639261435…06497960821931031971
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.960 Γ— 10⁹³(94-digit number)
49609928209278522870…12995921643862063941
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.921 Γ— 10⁹³(94-digit number)
99219856418557045740…25991843287724127881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.984 Γ— 10⁹⁴(95-digit number)
19843971283711409148…51983686575448255761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.968 Γ— 10⁹⁴(95-digit number)
39687942567422818296…03967373150896511521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.937 Γ— 10⁹⁴(95-digit number)
79375885134845636592…07934746301793023041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.587 Γ— 10⁹⁡(96-digit number)
15875177026969127318…15869492603586046081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.175 Γ— 10⁹⁡(96-digit number)
31750354053938254637…31738985207172092161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.350 Γ— 10⁹⁡(96-digit number)
63500708107876509274…63477970414344184321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.270 Γ— 10⁹⁢(97-digit number)
12700141621575301854…26955940828688368641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.540 Γ— 10⁹⁢(97-digit number)
25400283243150603709…53911881657376737281
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:58,006,831 XPMΒ·at block #6,845,298 Β· updates every 60s
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