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Block #676,850

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/13/2014, 11:59:53 PM Β· Difficulty 10.9649 Β· 6,125,836 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2b5838f471936e9d3c3d9611dc167529f83095e5821194f3e896611bc8dd92e8
View on Chainz β†—

Height

#676,850

Difficulty

10.964865

Transactions

2

Size

879 B

Version

2

Bits

0af7015f

Nonce

9,040

Timestamp

8/13/2014, 11:59:53 PM

Confirmations

6,125,836

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e5a44008bc17b9caf10d53439304c099328848e7637bc9493ce584225bbeea54
Transactions (2)
Coinbase971d35d2d23135…4a6905f6c9ea10
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
fd01bc78e403a3…64abd1e2f23757
4 in β†’ 2 out999.9200 XPM672 B
Ab2PravB…vdQHZsbdAbS5vujk…79omefUD
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.

2.164 Γ— 10⁹⁷(98-digit number)
21643885034504792618…46279114343158811581
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
2.164 Γ— 10⁹⁷(98-digit number)
21643885034504792618…46279114343158811581
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.328 Γ— 10⁹⁷(98-digit number)
43287770069009585236…92558228686317623161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.657 Γ— 10⁹⁷(98-digit number)
86575540138019170472…85116457372635246321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.731 Γ— 10⁹⁸(99-digit number)
17315108027603834094…70232914745270492641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.463 Γ— 10⁹⁸(99-digit number)
34630216055207668189…40465829490540985281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.926 Γ— 10⁹⁸(99-digit number)
69260432110415336378…80931658981081970561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.385 Γ— 10⁹⁹(100-digit number)
13852086422083067275…61863317962163941121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.770 Γ— 10⁹⁹(100-digit number)
27704172844166134551…23726635924327882241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.540 Γ— 10⁹⁹(100-digit number)
55408345688332269102…47453271848655764481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.108 Γ— 10¹⁰⁰(101-digit number)
11081669137666453820…94906543697311528961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.216 Γ— 10¹⁰⁰(101-digit number)
22163338275332907641…89813087394623057921
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:57,665,510 XPMΒ·at block #6,802,685 Β· updates every 60s
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