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Block #1,680,793

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/19/2016, 11:16:16 PM Β· Difficulty 10.7106 Β· 5,161,359 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1826c2290f845a8fb9da84fa0ee98c4b11ac6c33b31b5f56f48348e6efbc68e6
View on Chainz β†—

Height

#1,680,793

Difficulty

10.710575

Transactions

1

Size

200 B

Version

2

Bits

0ab5e83c

Nonce

332,395,792

Timestamp

7/19/2016, 11:16:16 PM

Confirmations

5,161,359

Mined by

⛏️ P2SHAJjasr3D41fZsoNFxDPmQBpcZHhkMZnu8r

Merkle Root

779f91213eaab8ddaa8102cad8a2e20f74103a56a08c45661d23f7321926ea2a
Transactions (1)
Coinbase779f91213eaab8…23f7321926ea2a
1 in β†’ 1 out8.7000 XPM109 B
AJjasr3D…hkMZnu8r
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.

3.040 Γ— 10⁹⁢(97-digit number)
30409282383038768400…82498262465026283521
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
3.040 Γ— 10⁹⁢(97-digit number)
30409282383038768400…82498262465026283521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.081 Γ— 10⁹⁢(97-digit number)
60818564766077536801…64996524930052567041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.216 Γ— 10⁹⁷(98-digit number)
12163712953215507360…29993049860105134081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.432 Γ— 10⁹⁷(98-digit number)
24327425906431014720…59986099720210268161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.865 Γ— 10⁹⁷(98-digit number)
48654851812862029441…19972199440420536321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.730 Γ— 10⁹⁷(98-digit number)
97309703625724058882…39944398880841072641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.946 Γ— 10⁹⁸(99-digit number)
19461940725144811776…79888797761682145281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.892 Γ— 10⁹⁸(99-digit number)
38923881450289623553…59777595523364290561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.784 Γ— 10⁹⁸(99-digit number)
77847762900579247106…19555191046728581121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.556 Γ— 10⁹⁹(100-digit number)
15569552580115849421…39110382093457162241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.113 Γ— 10⁹⁹(100-digit number)
31139105160231698842…78220764186914324481
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:57,981,605 XPMΒ·at block #6,842,151 Β· updates every 60s
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