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Block #2,844,601

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/18/2018, 8:28:14 AM Β· Difficulty 11.7280 Β· 3,989,253 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
f4d655a1a66405543d6a488f0946a9c136ab96bb3060a3566b4f8ac376c45460
View on Chainz β†—

Height

#2,844,601

Difficulty

11.728014

Transactions

1

Size

202 B

Version

2

Bits

0bba5f1a

Nonce

2,097,787,509

Timestamp

9/18/2018, 8:28:14 AM

Confirmations

3,989,253

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

6261e7bd8d3b72381d72c93224d47c6c7ad1928e6ad9ac39ea608e414b2090c7
Transactions (1)
Coinbase6261e7bd8d3b72…608e414b2090c7
1 in β†’ 1 out7.2600 XPM110 B
AZtxQr2F…7grUWrUz
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.

5.221 Γ— 10⁹⁸(99-digit number)
52217365029374202429…76451499924856831999
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
5.221 Γ— 10⁹⁸(99-digit number)
52217365029374202429…76451499924856831999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.221 Γ— 10⁹⁸(99-digit number)
52217365029374202429…76451499924856832001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.044 Γ— 10⁹⁹(100-digit number)
10443473005874840485…52902999849713663999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.044 Γ— 10⁹⁹(100-digit number)
10443473005874840485…52902999849713664001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.088 Γ— 10⁹⁹(100-digit number)
20886946011749680971…05805999699427327999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.088 Γ— 10⁹⁹(100-digit number)
20886946011749680971…05805999699427328001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.177 Γ— 10⁹⁹(100-digit number)
41773892023499361943…11611999398854655999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.177 Γ— 10⁹⁹(100-digit number)
41773892023499361943…11611999398854656001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
8.354 Γ— 10⁹⁹(100-digit number)
83547784046998723886…23223998797709311999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.354 Γ— 10⁹⁹(100-digit number)
83547784046998723886…23223998797709312001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.670 Γ— 10¹⁰⁰(101-digit number)
16709556809399744777…46447997595418623999
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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,915,063 XPMΒ·at block #6,833,853 Β· updates every 60s
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