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Block #787,449

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/29/2014, 1:46:09 AM Β· Difficulty 10.9746 Β· 6,022,386 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8eeb18b5d73a97ee87cd04c6d2a60c8ae9d0a3b3f7fe444a4e2eb4094bf704e6
View on Chainz β†—

Height

#787,449

Difficulty

10.974606

Transactions

2

Size

694 B

Version

2

Bits

0af97fc8

Nonce

106,377,900

Timestamp

10/29/2014, 1:46:09 AM

Confirmations

6,022,386

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cad4f934235203e9fed2591fc123054e65d5eaa27b864bfeb6e4cf54f4715e81
Transactions (2)
Coinbase2255687958fc57…2dbf4b1827a94d
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
618f2205a5c57d…0046b358ff99aa
3 in β†’ 1 out1149.9000 XPM488 B
APaT1yTL…GJCVsw9h
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.

2.402 Γ— 10⁹⁡(96-digit number)
24029967619306951985…73308286600332357441
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
2.402 Γ— 10⁹⁡(96-digit number)
24029967619306951985…73308286600332357441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.805 Γ— 10⁹⁡(96-digit number)
48059935238613903971…46616573200664714881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.611 Γ— 10⁹⁡(96-digit number)
96119870477227807942…93233146401329429761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.922 Γ— 10⁹⁢(97-digit number)
19223974095445561588…86466292802658859521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.844 Γ— 10⁹⁢(97-digit number)
38447948190891123176…72932585605317719041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.689 Γ— 10⁹⁢(97-digit number)
76895896381782246353…45865171210635438081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.537 Γ— 10⁹⁷(98-digit number)
15379179276356449270…91730342421270876161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.075 Γ— 10⁹⁷(98-digit number)
30758358552712898541…83460684842541752321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.151 Γ— 10⁹⁷(98-digit number)
61516717105425797082…66921369685083504641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.230 Γ— 10⁹⁸(99-digit number)
12303343421085159416…33842739370167009281
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:57,722,766 XPMΒ·at block #6,809,834 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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