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Block #10,916

2CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/11/2013, 4:49:47 AM Β· Difficulty 7.6949 Β· 6,797,395 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
df84790ac5921fa38d0694573ef2eb8eb78e44a7b91e8d126d994ddf564c010a
View on Chainz β†—

Height

#10,916

Difficulty

7.694923

Transactions

2

Size

848 B

Version

2

Bits

07b1e671

Nonce

176

Timestamp

7/11/2013, 4:49:47 AM

Confirmations

6,797,395

Mined by

⛏️ P2SHAeT98xFRhKHtTmvY77Vc7nzgBzLS7YHynv

Merkle Root

04a2cfdfea48245b516f829fc06736b31ee7931eb443eab7fd7aef8c5dba4109
Transactions (2)
Coinbase7bb975ceeaae06…86eea467498d37
1 in β†’ 1 out16.8800 XPM108 B
AeT98xFR…LS7YHynv
3781db4e416f55…f4b728a6c9dd89
5 in β†’ 1 out77.6300 XPM649 B
AQMR94ur…S8cLWAU3
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.

2.202 Γ— 10⁹⁢(97-digit number)
22023761433271501330…72627727790797404831
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
2.202 Γ— 10⁹⁢(97-digit number)
22023761433271501330…72627727790797404831
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.404 Γ— 10⁹⁢(97-digit number)
44047522866543002660…45255455581594809661
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.809 Γ— 10⁹⁢(97-digit number)
88095045733086005320…90510911163189619321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.761 Γ— 10⁹⁷(98-digit number)
17619009146617201064…81021822326379238641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.523 Γ— 10⁹⁷(98-digit number)
35238018293234402128…62043644652758477281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.047 Γ— 10⁹⁷(98-digit number)
70476036586468804256…24087289305516954561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.409 Γ— 10⁹⁸(99-digit number)
14095207317293760851…48174578611033909121
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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
CommonChain length 7

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,710,540 XPMΒ·at block #6,808,310 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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