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Block #2,751,135

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/16/2018, 8:22:30 AM Β· Difficulty 11.6445 Β· 4,082,028 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
70d2f8f5b6f2c37258baf634798a8d26eb8f6232ad892019d681118451530921
View on Chainz β†—

Height

#2,751,135

Difficulty

11.644457

Transactions

2

Size

1.83 KB

Version

2

Bits

0ba4fb1c

Nonce

459,856,480

Timestamp

7/16/2018, 8:22:30 AM

Confirmations

4,082,028

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

ba4f8f12f4638a9fa7b5a0fdd1f10387f520bc179f566fa5ffa8c7523b4fe552
Transactions (2)
Coinbasec8545d75e93a82…1470f2eb051c9a
1 in β†’ 1 out7.3800 XPM109 B
AZtxQr2F…7grUWrUz
3df12458eb96ea…541100dbfc132f
11 in β†’ 1 out9962.8600 XPM1.64 KB
AU4MBGBZ…vqkBE1Y2
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.

3.599 Γ— 10⁹⁹(100-digit number)
35991791663309197214…36569967946023567359
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
3.599 Γ— 10⁹⁹(100-digit number)
35991791663309197214…36569967946023567359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.599 Γ— 10⁹⁹(100-digit number)
35991791663309197214…36569967946023567361
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
7.198 Γ— 10⁹⁹(100-digit number)
71983583326618394429…73139935892047134719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.198 Γ— 10⁹⁹(100-digit number)
71983583326618394429…73139935892047134721
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
1.439 Γ— 10¹⁰⁰(101-digit number)
14396716665323678885…46279871784094269439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.439 Γ— 10¹⁰⁰(101-digit number)
14396716665323678885…46279871784094269441
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
2.879 Γ— 10¹⁰⁰(101-digit number)
28793433330647357771…92559743568188538879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.879 Γ— 10¹⁰⁰(101-digit number)
28793433330647357771…92559743568188538881
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
5.758 Γ— 10¹⁰⁰(101-digit number)
57586866661294715543…85119487136377077759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.758 Γ— 10¹⁰⁰(101-digit number)
57586866661294715543…85119487136377077761
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
1.151 Γ— 10¹⁰¹(102-digit number)
11517373332258943108…70238974272754155519
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:57,909,484 XPMΒ·at block #6,833,162 Β· updates every 60s
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