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Block #1,973,925

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/8/2017, 2:25:21 AM Β· Difficulty 10.7549 Β· 4,859,816 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4c56c1b9e80c656d22655b5962e32364160e1e1e7dc74bf0fbc78f1015d5dca0
View on Chainz β†—

Height

#1,973,925

Difficulty

10.754864

Transactions

2

Size

686 B

Version

2

Bits

0ac13ec4

Nonce

1,053,205,506

Timestamp

2/8/2017, 2:25:21 AM

Confirmations

4,859,816

Mined by

⛏️ P2SHAGWJ7M8D8ySgXuuusM2oaGVpXdbYDnEf7w

Merkle Root

6f4c3b98750be83720aad9ecf7b2c1fa758fe524bec09b48f7daed2dc1bc7827
Transactions (2)
Coinbase2c8d5705cb21f8…14c9cea4c5859c
1 in β†’ 1 out8.6400 XPM110 B
AGWJ7M8D…bYDnEf7w
9ee350adacb1e6…54ca74353ed959
3 in β†’ 1 out2.0871 XPM486 B
AKjgCpST…no8iVVii
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.

9.895 Γ— 10⁹³(94-digit number)
98958686361981371463…35423917047036271441
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
9.895 Γ— 10⁹³(94-digit number)
98958686361981371463…35423917047036271441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.979 Γ— 10⁹⁴(95-digit number)
19791737272396274292…70847834094072542881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.958 Γ— 10⁹⁴(95-digit number)
39583474544792548585…41695668188145085761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.916 Γ— 10⁹⁴(95-digit number)
79166949089585097170…83391336376290171521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.583 Γ— 10⁹⁡(96-digit number)
15833389817917019434…66782672752580343041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.166 Γ— 10⁹⁡(96-digit number)
31666779635834038868…33565345505160686081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.333 Γ— 10⁹⁡(96-digit number)
63333559271668077736…67130691010321372161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.266 Γ— 10⁹⁢(97-digit number)
12666711854333615547…34261382020642744321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.533 Γ— 10⁹⁢(97-digit number)
25333423708667231094…68522764041285488641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.066 Γ— 10⁹⁢(97-digit number)
50666847417334462189…37045528082570977281
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:57,914,146 XPMΒ·at block #6,833,740 Β· updates every 60s
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