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Block #2,762,364

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/24/2018, 1:08:18 AM Β· Difficulty 11.6549 Β· 4,078,468 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b98e1f8e56d2dedaddb88ba69da7aee8185e18e2f43fe6a76d75368e53768678
View on Chainz β†—

Height

#2,762,364

Difficulty

11.654858

Transactions

2

Size

2.88 KB

Version

2

Bits

0ba7a4c9

Nonce

371,773,309

Timestamp

7/24/2018, 1:08:18 AM

Confirmations

4,078,468

Mined by

⛏️ P2SHAdpQRorjw5mTc3RfkYEfvtn1C3QFuBp2JJ

Merkle Root

366eda9958e50f392cd496e86d003ad83db2c97d2a78ee030647a5b153811570
Transactions (2)
Coinbaseb26583e9775db5…52c5a81160c63d
1 in β†’ 1 out7.3800 XPM110 B
AdpQRorj…QFuBp2JJ
2c994aaac4781c…4773567de29701
18 in β†’ 2 out16441.8290 XPM2.68 KB
AVk5F2RE…34mEffPFAUnZUVKQ…ef4ferXq
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.

1.026 Γ— 10⁹⁷(98-digit number)
10261988904012299963…64377835146895999999
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
1.026 Γ— 10⁹⁷(98-digit number)
10261988904012299963…64377835146895999999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.026 Γ— 10⁹⁷(98-digit number)
10261988904012299963…64377835146896000001
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
2.052 Γ— 10⁹⁷(98-digit number)
20523977808024599926…28755670293791999999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.052 Γ— 10⁹⁷(98-digit number)
20523977808024599926…28755670293792000001
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
4.104 Γ— 10⁹⁷(98-digit number)
41047955616049199853…57511340587583999999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.104 Γ— 10⁹⁷(98-digit number)
41047955616049199853…57511340587584000001
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
8.209 Γ— 10⁹⁷(98-digit number)
82095911232098399706…15022681175167999999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.209 Γ— 10⁹⁷(98-digit number)
82095911232098399706…15022681175168000001
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
1.641 Γ— 10⁹⁸(99-digit number)
16419182246419679941…30045362350335999999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.641 Γ— 10⁹⁸(99-digit number)
16419182246419679941…30045362350336000001
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
3.283 Γ— 10⁹⁸(99-digit number)
32838364492839359882…60090724700671999999
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:57,971,002 XPMΒ·at block #6,840,831 Β· updates every 60s
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