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Block #2,706,712

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/15/2018, 8:03:14 PM Β· Difficulty 11.6070 Β· 4,124,835 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3ef197ceecf22afb0ee9f9d1917ba3bfdc844c5dd5b8332d8b64786ecaf39d78
View on Chainz β†—

Height

#2,706,712

Difficulty

11.606981

Transactions

2

Size

869 B

Version

2

Bits

0b9b6318

Nonce

229,720,402

Timestamp

6/15/2018, 8:03:14 PM

Confirmations

4,124,835

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

08b83ee0f89d76fca4deaf8c2fe443f2a8f587901d4ef8e8aeb84bec56896abf
Transactions (2)
Coinbase61ec69d8dc6705…5b95b757d4ab3a
1 in β†’ 1 out7.4200 XPM110 B
AZtxQr2F…7grUWrUz
0e386185b15f31…d7c792c0d821c7
4 in β†’ 2 out2729.0099 XPM669 B
AGs3bDdD…sVceRfWaAeh6H5Th…PrPMi2xx
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.

1.312 Γ— 10⁹⁡(96-digit number)
13128794109408248594…80075349026524445441
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
1.312 Γ— 10⁹⁡(96-digit number)
13128794109408248594…80075349026524445441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.625 Γ— 10⁹⁡(96-digit number)
26257588218816497188…60150698053048890881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.251 Γ— 10⁹⁡(96-digit number)
52515176437632994377…20301396106097781761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.050 Γ— 10⁹⁢(97-digit number)
10503035287526598875…40602792212195563521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.100 Γ— 10⁹⁢(97-digit number)
21006070575053197750…81205584424391127041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.201 Γ— 10⁹⁢(97-digit number)
42012141150106395501…62411168848782254081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.402 Γ— 10⁹⁢(97-digit number)
84024282300212791003…24822337697564508161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.680 Γ— 10⁹⁷(98-digit number)
16804856460042558200…49644675395129016321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.360 Γ— 10⁹⁷(98-digit number)
33609712920085116401…99289350790258032641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.721 Γ— 10⁹⁷(98-digit number)
67219425840170232802…98578701580516065281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.344 Γ— 10⁹⁸(99-digit number)
13443885168034046560…97157403161032130561
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:57,896,467 XPMΒ·at block #6,831,546 Β· updates every 60s
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