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Block #10,556

2CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/11/2013, 3:26:56 AM Β· Difficulty 7.6777 Β· 6,791,240 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d4ea872f8d6c82c1a25a542c60d379de3c048c55784b42f04e43eb5b8876b192
View on Chainz β†—

Height

#10,556

Difficulty

7.677672

Transactions

1

Size

199 B

Version

2

Bits

07ad7be8

Nonce

75

Timestamp

7/11/2013, 3:26:56 AM

Confirmations

6,791,240

Mined by

⛏️ P2SHAM6VRLKvWNLUn43QLb3EuhPjXzByN91i1u

Merkle Root

2cfa07bdfb230b3c1018840cab09e60951fcaca45460b9bf30d4334fad0682ff
Transactions (1)
Coinbase2cfa07bdfb230b…d4334fad0682ff
1 in β†’ 1 out16.9400 XPM109 B
AM6VRLKv…ByN91i1u
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.

7.054 Γ— 10⁹⁴(95-digit number)
70546990999150954847…18690965300276957201
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
7.054 Γ— 10⁹⁴(95-digit number)
70546990999150954847…18690965300276957201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.410 Γ— 10⁹⁡(96-digit number)
14109398199830190969…37381930600553914401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.821 Γ— 10⁹⁡(96-digit number)
28218796399660381938…74763861201107828801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.643 Γ— 10⁹⁡(96-digit number)
56437592799320763877…49527722402215657601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.128 Γ— 10⁹⁢(97-digit number)
11287518559864152775…99055444804431315201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.257 Γ— 10⁹⁢(97-digit number)
22575037119728305551…98110889608862630401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.515 Γ— 10⁹⁢(97-digit number)
45150074239456611102…96221779217725260801
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:57,658,458 XPMΒ·at block #6,801,795 Β· updates every 60s
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