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Block #2,771,892

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/30/2018, 2:19:25 PM Β· Difficulty 11.6617 Β· 4,073,097 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e55b655b59563a0f2dc8fc33681e918e7ce38bdcd30498e3fc876b2a25a32e9d
View on Chainz β†—

Height

#2,771,892

Difficulty

11.661696

Transactions

2

Size

392 B

Version

2

Bits

0ba964e2

Nonce

278,350,228

Timestamp

7/30/2018, 2:19:25 PM

Confirmations

4,073,097

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

f1678e4151c00936bd05435e7c6aa681fb63ebe61c78a034712757811ca4b813
Transactions (2)
Coinbaseb938d009bde3e8…f94a62bf6e326f
1 in β†’ 1 out7.3500 XPM110 B
AZtxQr2F…7grUWrUz
bc82b576125849…2e0623527ea228
1 in β†’ 2 out7.3200 XPM192 B
ASQdb5nP…7oSVGsmbAPzzZCMi…JnPuaAnx
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.

1.447 Γ— 10⁹⁡(96-digit number)
14472821663044131209…91826365100472089621
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
1.447 Γ— 10⁹⁡(96-digit number)
14472821663044131209…91826365100472089621
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.894 Γ— 10⁹⁡(96-digit number)
28945643326088262418…83652730200944179241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.789 Γ— 10⁹⁡(96-digit number)
57891286652176524837…67305460401888358481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.157 Γ— 10⁹⁢(97-digit number)
11578257330435304967…34610920803776716961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.315 Γ— 10⁹⁢(97-digit number)
23156514660870609934…69221841607553433921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.631 Γ— 10⁹⁢(97-digit number)
46313029321741219869…38443683215106867841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.262 Γ— 10⁹⁢(97-digit number)
92626058643482439739…76887366430213735681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.852 Γ— 10⁹⁷(98-digit number)
18525211728696487947…53774732860427471361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.705 Γ— 10⁹⁷(98-digit number)
37050423457392975895…07549465720854942721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.410 Γ— 10⁹⁷(98-digit number)
74100846914785951791…15098931441709885441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.482 Γ— 10⁹⁸(99-digit number)
14820169382957190358…30197862883419770881
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:58,004,331 XPMΒ·at block #6,844,988 Β· updates every 60s
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