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Block #2,647,750

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/4/2018, 2:36:15 AM Β· Difficulty 11.7622 Β· 4,191,527 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
83ce1f308f0e20036ae2f8c6ea7a7c46fc10e085cc336630636aa563a72ba70d
View on Chainz β†—

Height

#2,647,750

Difficulty

11.762171

Transactions

1

Size

202 B

Version

2

Bits

0bc31da6

Nonce

534,214,844

Timestamp

5/4/2018, 2:36:15 AM

Confirmations

4,191,527

Mined by

⛏️ P2SHAQoVZ45saAwWDTYZbJ4cUJ6kJvDUHidWj1

Merkle Root

42b5a28742d13c4d2df3be9444e20ed01a2a7fd0a792a7ba9f094175672004a9
Transactions (1)
Coinbase42b5a28742d13c…094175672004a9
1 in β†’ 1 out7.2200 XPM110 B
AQoVZ45s…DUHidWj1
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.

5.645 Γ— 10⁹⁸(99-digit number)
56453988425562478316…51691949604198154239
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
5.645 Γ— 10⁹⁸(99-digit number)
56453988425562478316…51691949604198154239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.645 Γ— 10⁹⁸(99-digit number)
56453988425562478316…51691949604198154241
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
1.129 Γ— 10⁹⁹(100-digit number)
11290797685112495663…03383899208396308479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.129 Γ— 10⁹⁹(100-digit number)
11290797685112495663…03383899208396308481
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
2.258 Γ— 10⁹⁹(100-digit number)
22581595370224991326…06767798416792616959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.258 Γ— 10⁹⁹(100-digit number)
22581595370224991326…06767798416792616961
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
4.516 Γ— 10⁹⁹(100-digit number)
45163190740449982653…13535596833585233919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.516 Γ— 10⁹⁹(100-digit number)
45163190740449982653…13535596833585233921
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
9.032 Γ— 10⁹⁹(100-digit number)
90326381480899965307…27071193667170467839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.032 Γ— 10⁹⁹(100-digit number)
90326381480899965307…27071193667170467841
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
1.806 Γ— 10¹⁰⁰(101-digit number)
18065276296179993061…54142387334340935679
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:57,958,501 XPMΒ·at block #6,839,276 Β· updates every 60s
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