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Block #2,848,590

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/21/2018, 1:30:31 AM Β· Difficulty 11.7328 Β· 3,984,082 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e201c224414d42e478852d6d77fd45a0dadd3027dbb9fde3de467cf27ae207cb
View on Chainz β†—

Height

#2,848,590

Difficulty

11.732829

Transactions

2

Size

6.63 KB

Version

2

Bits

0bbb9ab3

Nonce

288,044,450

Timestamp

9/21/2018, 1:30:31 AM

Confirmations

3,984,082

Mined by

⛏️ P2SHAM1tqa5zHXYKsUWjWExNnDXtLVXudXdok8

Merkle Root

210e395796ff0740a00e8603f1914eb2ce986528a02464aa6d134a3093d38fed
Transactions (2)
Coinbase628dc2ab80fdd0…c206bfb699480d
1 in β†’ 1 out7.3500 XPM110 B
AM1tqa5z…XudXdok8
906dc0ee01a856…ac152688f2685a
44 in β†’ 2 out9998.0100 XPM6.44 KB
AKNrq3g4…GWp8pZ4HARuzC2fn…HxRDPrx7
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.

3.093 Γ— 10⁹³(94-digit number)
30930767131053714320…94006887763168816649
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
3.093 Γ— 10⁹³(94-digit number)
30930767131053714320…94006887763168816649
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.093 Γ— 10⁹³(94-digit number)
30930767131053714320…94006887763168816651
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
6.186 Γ— 10⁹³(94-digit number)
61861534262107428640…88013775526337633299
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.186 Γ— 10⁹³(94-digit number)
61861534262107428640…88013775526337633301
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
1.237 Γ— 10⁹⁴(95-digit number)
12372306852421485728…76027551052675266599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.237 Γ— 10⁹⁴(95-digit number)
12372306852421485728…76027551052675266601
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
2.474 Γ— 10⁹⁴(95-digit number)
24744613704842971456…52055102105350533199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.474 Γ— 10⁹⁴(95-digit number)
24744613704842971456…52055102105350533201
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
4.948 Γ— 10⁹⁴(95-digit number)
49489227409685942912…04110204210701066399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.948 Γ— 10⁹⁴(95-digit number)
49489227409685942912…04110204210701066401
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
9.897 Γ— 10⁹⁴(95-digit number)
98978454819371885825…08220408421402132799
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:57,905,528 XPMΒ·at block #6,832,671 Β· updates every 60s
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