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Block #2,125,938

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/20/2017, 9:52:34 PM Β· Difficulty 10.9193 Β· 4,716,316 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2ce79c13c1f98c3013b2e09986fb7ec6093a385adce80f689719f1edc3a40fb3
View on Chainz β†—

Height

#2,125,938

Difficulty

10.919251

Transactions

1

Size

242 B

Version

2

Bits

0aeb540e

Nonce

993,565,043

Timestamp

5/20/2017, 9:52:34 PM

Confirmations

4,716,316

Mined by

⛏️ P2SHAMMJ7Ku9ctFmjCbBPtKsnh34K5ZYGbYo5z

Merkle Root

ab8d0d4e2e700899031e63f8d8b67d2a208a8922559bca5b8f4922185f430eea
Transactions (1)
Coinbaseab8d0d4e2e7008…4922185f430eea
1 in β†’ 2 out8.3700 XPM152 B
AMMJ7Ku9…ZYGbYo5zAXbk7f7A…Tx7JECPG
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.

1.045 Γ— 10⁹⁡(96-digit number)
10453337331308005298…67679125771777778521
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
1.045 Γ— 10⁹⁡(96-digit number)
10453337331308005298…67679125771777778521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.090 Γ— 10⁹⁡(96-digit number)
20906674662616010597…35358251543555557041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.181 Γ— 10⁹⁡(96-digit number)
41813349325232021194…70716503087111114081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.362 Γ— 10⁹⁡(96-digit number)
83626698650464042388…41433006174222228161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.672 Γ— 10⁹⁢(97-digit number)
16725339730092808477…82866012348444456321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.345 Γ— 10⁹⁢(97-digit number)
33450679460185616955…65732024696888912641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.690 Γ— 10⁹⁢(97-digit number)
66901358920371233911…31464049393777825281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.338 Γ— 10⁹⁷(98-digit number)
13380271784074246782…62928098787555650561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.676 Γ— 10⁹⁷(98-digit number)
26760543568148493564…25856197575111301121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.352 Γ— 10⁹⁷(98-digit number)
53521087136296987128…51712395150222602241
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:57,982,429 XPMΒ·at block #6,842,253 Β· updates every 60s
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