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Block #207,846

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/13/2013, 4:21:43 PM Β· Difficulty 9.9042 Β· 6,619,172 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
da9cc07885f7ab25e3335bc83b88e9f70acca36bb21dd2e0318c6defc4d3e576
View on Chainz β†—

Height

#207,846

Difficulty

9.904210

Transactions

1

Size

198 B

Version

2

Bits

09e77a4d

Nonce

34,893

Timestamp

10/13/2013, 4:21:43 PM

Confirmations

6,619,172

Mined by

⛏️ P2SHAbJUC2oSrZY84nuu7WUoHPgJjAcpKam6LK

Merkle Root

43e757430ba0ad99fbc0fbb6fc52505fe7471252f700889d8b17fd99de373ee4
Transactions (1)
Coinbase43e757430ba0ad…17fd99de373ee4
1 in β†’ 1 out10.1800 XPM109 B
AbJUC2oS…cpKam6LK
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.

3.312 Γ— 10⁹³(94-digit number)
33120260392861673930…17439663637770025821
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
3.312 Γ— 10⁹³(94-digit number)
33120260392861673930…17439663637770025821
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.624 Γ— 10⁹³(94-digit number)
66240520785723347861…34879327275540051641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.324 Γ— 10⁹⁴(95-digit number)
13248104157144669572…69758654551080103281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.649 Γ— 10⁹⁴(95-digit number)
26496208314289339144…39517309102160206561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.299 Γ— 10⁹⁴(95-digit number)
52992416628578678288…79034618204320413121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.059 Γ— 10⁹⁡(96-digit number)
10598483325715735657…58069236408640826241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.119 Γ— 10⁹⁡(96-digit number)
21196966651431471315…16138472817281652481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.239 Γ— 10⁹⁡(96-digit number)
42393933302862942631…32276945634563304961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.478 Γ— 10⁹⁡(96-digit number)
84787866605725885262…64553891269126609921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.695 Γ— 10⁹⁢(97-digit number)
16957573321145177052…29107782538253219841
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:57,860,322 XPMΒ·at block #6,827,017 Β· updates every 60s
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