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Block #2,654,974

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/9/2018, 7:16:39 PM Β· Difficulty 11.7117 Β· 4,187,451 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eb841757d9f7c3f9a6f564b03ab6898ab200e386d737c7285a8b822fcceeb7e3
View on Chainz β†—

Height

#2,654,974

Difficulty

11.711655

Transactions

1

Size

201 B

Version

2

Bits

0bb62efe

Nonce

1,032,617,512

Timestamp

5/9/2018, 7:16:39 PM

Confirmations

4,187,451

Mined by

⛏️ P2SHATBGxdde1shRYjHZA25krDmidHqGyKrxBz

Merkle Root

878b222891d36f1532faf1d128cc745d7be248a3987f70d7af26de84b10a7863
Transactions (1)
Coinbase878b222891d36f…26de84b10a7863
1 in β†’ 1 out7.2800 XPM110 B
ATBGxdde…qGyKrxBz
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.

1.043 Γ— 10⁹⁷(98-digit number)
10431018709290451729…49609562650930391041
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
1.043 Γ— 10⁹⁷(98-digit number)
10431018709290451729…49609562650930391041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.086 Γ— 10⁹⁷(98-digit number)
20862037418580903459…99219125301860782081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.172 Γ— 10⁹⁷(98-digit number)
41724074837161806918…98438250603721564161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.344 Γ— 10⁹⁷(98-digit number)
83448149674323613836…96876501207443128321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.668 Γ— 10⁹⁸(99-digit number)
16689629934864722767…93753002414886256641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.337 Γ— 10⁹⁸(99-digit number)
33379259869729445534…87506004829772513281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.675 Γ— 10⁹⁸(99-digit number)
66758519739458891069…75012009659545026561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.335 Γ— 10⁹⁹(100-digit number)
13351703947891778213…50024019319090053121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.670 Γ— 10⁹⁹(100-digit number)
26703407895783556427…00048038638180106241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.340 Γ— 10⁹⁹(100-digit number)
53406815791567112855…00096077276360212481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.068 Γ— 10¹⁰⁰(101-digit number)
10681363158313422571…00192154552720424961
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:57,983,815 XPMΒ·at block #6,842,424 Β· updates every 60s
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