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Block #2,840,451

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/15/2018, 1:43:12 PM Β· Difficulty 11.7200 Β· 4,004,940 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
969f95b736532b5f341b222629dd04ae86489fb886b21f140db42f469624581d
View on Chainz β†—

Height

#2,840,451

Difficulty

11.719963

Transactions

1

Size

200 B

Version

2

Bits

0bb84f78

Nonce

1,026,695,678

Timestamp

9/15/2018, 1:43:12 PM

Confirmations

4,004,940

Mined by

⛏️ P2SHAbjsXQ6Dn5Z1wz9pPUobmiUUKiKdmzwcxr

Merkle Root

bbb039d86de05a545747af3af0f0f9f12abec01f0018f53c0b4b3938d76ef2e5
Transactions (1)
Coinbasebbb039d86de05a…4b3938d76ef2e5
1 in β†’ 1 out7.2700 XPM110 B
AbjsXQ6D…Kdmzwcxr
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.

1.905 Γ— 10⁹⁡(96-digit number)
19055498662984791547…09769148432392611761
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
1.905 Γ— 10⁹⁡(96-digit number)
19055498662984791547…09769148432392611761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.811 Γ— 10⁹⁡(96-digit number)
38110997325969583094…19538296864785223521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.622 Γ— 10⁹⁡(96-digit number)
76221994651939166189…39076593729570447041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.524 Γ— 10⁹⁢(97-digit number)
15244398930387833237…78153187459140894081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.048 Γ— 10⁹⁢(97-digit number)
30488797860775666475…56306374918281788161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.097 Γ— 10⁹⁢(97-digit number)
60977595721551332951…12612749836563576321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.219 Γ— 10⁹⁷(98-digit number)
12195519144310266590…25225499673127152641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.439 Γ— 10⁹⁷(98-digit number)
24391038288620533180…50450999346254305281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.878 Γ— 10⁹⁷(98-digit number)
48782076577241066361…00901998692508610561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.756 Γ— 10⁹⁷(98-digit number)
97564153154482132723…01803997385017221121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.951 Γ— 10⁹⁸(99-digit number)
19512830630896426544…03607994770034442241
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:58,007,574 XPMΒ·at block #6,845,390 Β· updates every 60s
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