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Block #2,177,338

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/25/2017, 12:33:26 PM Β· Difficulty 10.9224 Β· 4,665,017 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fff19d5f3509e2bd9083961a1a6e6e4afe8c2ea9c30817f2d0373c74c1b0848e
View on Chainz β†—

Height

#2,177,338

Difficulty

10.922440

Transactions

2

Size

765 B

Version

2

Bits

0aec2504

Nonce

96,599,376

Timestamp

6/25/2017, 12:33:26 PM

Confirmations

4,665,017

Mined by

⛏️ P2SHAYHZ4XCMsiiLUaDAMotbcrWS3WZes7Bskc

Merkle Root

bc4040ec3164fbc997fc551b923bb01f68e2dd346a23e35d9587305ae905e4e2
Transactions (2)
Coinbase2289c5decb3fa7…555268d51031c0
1 in β†’ 1 out8.3800 XPM109 B
AYHZ4XCM…Zes7Bskc
35f17e56290702…05547c844d0a92
4 in β†’ 2 out27.9052 XPM566 B
AdQVyW6h…woPp73cjAUy46zAJ…RjrJ2pJi
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.

1.190 Γ— 10⁹⁴(95-digit number)
11907976489218326620…72861728881316349081
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
1.190 Γ— 10⁹⁴(95-digit number)
11907976489218326620…72861728881316349081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.381 Γ— 10⁹⁴(95-digit number)
23815952978436653240…45723457762632698161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.763 Γ— 10⁹⁴(95-digit number)
47631905956873306480…91446915525265396321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.526 Γ— 10⁹⁴(95-digit number)
95263811913746612960…82893831050530792641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.905 Γ— 10⁹⁡(96-digit number)
19052762382749322592…65787662101061585281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.810 Γ— 10⁹⁡(96-digit number)
38105524765498645184…31575324202123170561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.621 Γ— 10⁹⁡(96-digit number)
76211049530997290368…63150648404246341121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.524 Γ— 10⁹⁢(97-digit number)
15242209906199458073…26301296808492682241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.048 Γ— 10⁹⁢(97-digit number)
30484419812398916147…52602593616985364481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.096 Γ— 10⁹⁢(97-digit number)
60968839624797832294…05205187233970728961
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,983,247 XPMΒ·at block #6,842,354 Β· updates every 60s
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