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Block #2,656,255

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/10/2018, 10:17:21 PM Β· Difficulty 11.6917 Β· 4,184,628 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
54395bb02087e793e2fa5bdc7f3a4b30fa7907a446c2bd9909f5f05bef0955d6
View on Chainz β†—

Height

#2,656,255

Difficulty

11.691719

Transactions

2

Size

392 B

Version

2

Bits

0bb11485

Nonce

1,525,763,352

Timestamp

5/10/2018, 10:17:21 PM

Confirmations

4,184,628

Mined by

⛏️ P2SHAP6PD3o1qiBxLsCJkWaKK6ns9dJUch9QMp

Merkle Root

011411a6aa11ec2f72a6d137debe065d7db638dfc3ea9a577a9799ebe525eed6
Transactions (2)
Coinbasef7634c9e5ebaaa…37c40c078866c6
1 in β†’ 1 out7.3100 XPM110 B
AP6PD3o1…JUch9QMp
606f204a5f818f…ef1b3794236a20
1 in β†’ 1 out0.9900 XPM192 B
AUxDHVPK…RCEhdJgF
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.

3.064 Γ— 10⁹⁴(95-digit number)
30642426763944311398…52004335344932043441
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
3.064 Γ— 10⁹⁴(95-digit number)
30642426763944311398…52004335344932043441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.128 Γ— 10⁹⁴(95-digit number)
61284853527888622796…04008670689864086881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.225 Γ— 10⁹⁡(96-digit number)
12256970705577724559…08017341379728173761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.451 Γ— 10⁹⁡(96-digit number)
24513941411155449118…16034682759456347521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.902 Γ— 10⁹⁡(96-digit number)
49027882822310898237…32069365518912695041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.805 Γ— 10⁹⁡(96-digit number)
98055765644621796474…64138731037825390081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.961 Γ— 10⁹⁢(97-digit number)
19611153128924359294…28277462075650780161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.922 Γ— 10⁹⁢(97-digit number)
39222306257848718589…56554924151301560321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.844 Γ— 10⁹⁢(97-digit number)
78444612515697437179…13109848302603120641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.568 Γ— 10⁹⁷(98-digit number)
15688922503139487435…26219696605206241281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.137 Γ— 10⁹⁷(98-digit number)
31377845006278974871…52439393210412482561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
6.275 Γ— 10⁹⁷(98-digit number)
62755690012557949743…04878786420824965121
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,971,413 XPMΒ·at block #6,840,882 Β· updates every 60s
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