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Block #2,005,199

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/2/2017, 6:56:19 AM Β· Difficulty 10.7214 Β· 4,831,654 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
349f92eb5ee4b5a22fe05262cbe94d31f697076e90c95b500a053babdcd9c609
View on Chainz β†—

Height

#2,005,199

Difficulty

10.721373

Transactions

2

Size

4.45 KB

Version

2

Bits

0ab8abef

Nonce

1,051,273,911

Timestamp

3/2/2017, 6:56:19 AM

Confirmations

4,831,654

Mined by

⛏️ P2SHAaHCbQdvgpq68gAuC9DwFfVfGW9jo5APT9

Merkle Root

468bbd2cf4513004114959a91b5c4881277a18dd356f0e42a1ab189b4c8f8de7
Transactions (2)
Coinbasec160f43132773b…9994a1210c897f
1 in β†’ 1 out8.7400 XPM109 B
AaHCbQdv…9jo5APT9
135eba77826a99…9369940faf05ad
29 in β†’ 2 out80.0100 XPM4.26 KB
AbwdBgUA…9cGN6KN8AUwo1vZj…93qAT7rY
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.

1.559 Γ— 10⁹⁴(95-digit number)
15594964712278950533…40868046758735980801
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
1.559 Γ— 10⁹⁴(95-digit number)
15594964712278950533…40868046758735980801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.118 Γ— 10⁹⁴(95-digit number)
31189929424557901066…81736093517471961601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.237 Γ— 10⁹⁴(95-digit number)
62379858849115802132…63472187034943923201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.247 Γ— 10⁹⁡(96-digit number)
12475971769823160426…26944374069887846401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.495 Γ— 10⁹⁡(96-digit number)
24951943539646320853…53888748139775692801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.990 Γ— 10⁹⁡(96-digit number)
49903887079292641706…07777496279551385601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.980 Γ— 10⁹⁡(96-digit number)
99807774158585283412…15554992559102771201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.996 Γ— 10⁹⁢(97-digit number)
19961554831717056682…31109985118205542401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.992 Γ— 10⁹⁢(97-digit number)
39923109663434113364…62219970236411084801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.984 Γ— 10⁹⁢(97-digit number)
79846219326868226729…24439940472822169601
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:57,939,112 XPMΒ·at block #6,836,852 Β· updates every 60s
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