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Block #2,284,636

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/6/2017, 8:11:15 AM Β· Difficulty 10.9551 Β· 4,557,617 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c45a39f2516dc0cca714dcf15d4dcf81636b93e8048f7707fd3b82b5cb709d40
View on Chainz β†—

Height

#2,284,636

Difficulty

10.955143

Transactions

1

Size

200 B

Version

2

Bits

0af48440

Nonce

1,130,860,302

Timestamp

9/6/2017, 8:11:15 AM

Confirmations

4,557,617

Mined by

⛏️ P2SHAJK6MyLy6hFFEV8615zLUjjA9cg5jN4nNB

Merkle Root

89dab37c78106f0f7c5f19d6c50f2f9bbae9526da0b91ef8119a04a0dd4e1d63
Transactions (1)
Coinbase89dab37c78106f…9a04a0dd4e1d63
1 in β†’ 1 out8.3200 XPM110 B
AJK6MyLy…g5jN4nNB
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.

6.207 Γ— 10⁹⁴(95-digit number)
62076971136983075166…29654405424571298079
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
6.207 Γ— 10⁹⁴(95-digit number)
62076971136983075166…29654405424571298079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.207 Γ— 10⁹⁴(95-digit number)
62076971136983075166…29654405424571298081
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
1.241 Γ— 10⁹⁡(96-digit number)
12415394227396615033…59308810849142596159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.241 Γ— 10⁹⁡(96-digit number)
12415394227396615033…59308810849142596161
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
2.483 Γ— 10⁹⁡(96-digit number)
24830788454793230066…18617621698285192319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.483 Γ— 10⁹⁡(96-digit number)
24830788454793230066…18617621698285192321
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
4.966 Γ— 10⁹⁡(96-digit number)
49661576909586460132…37235243396570384639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.966 Γ— 10⁹⁡(96-digit number)
49661576909586460132…37235243396570384641
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
9.932 Γ— 10⁹⁡(96-digit number)
99323153819172920265…74470486793140769279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.932 Γ— 10⁹⁡(96-digit number)
99323153819172920265…74470486793140769281
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
1.986 Γ— 10⁹⁢(97-digit number)
19864630763834584053…48940973586281538559
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:57,982,421 XPMΒ·at block #6,842,252 Β· updates every 60s
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