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Block #2,756,105

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/19/2018, 3:02:17 PM Β· Difficulty 11.6619 Β· 4,075,080 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5b17d568c0709b627db8ae8bdd865fd2705a1708ffccc4bff0839c1d62aa63e7
View on Chainz β†—

Height

#2,756,105

Difficulty

11.661867

Transactions

2

Size

722 B

Version

2

Bits

0ba9701e

Nonce

1,169,019,014

Timestamp

7/19/2018, 3:02:17 PM

Confirmations

4,075,080

Mined by

⛏️ P2SHAHnS4h4MBWRrmuQ5Ve7VwrW3WkdmoojMdV

Merkle Root

be2e019293030bb60f438ff7a4beea9d7bfc6b027648ac67c18069c8bffeebf4
Transactions (2)
Coinbase252b95a2559da0…6f1f2c5cd9f6b1
1 in β†’ 1 out7.3500 XPM110 B
AHnS4h4M…dmoojMdV
a095b6ab86a590…570983058b6f3a
3 in β†’ 2 out197.0965 XPM522 B
AMacMFhM…iFNVuut4AYEr4GLT…q79owHYX
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.

1.776 Γ— 10⁹⁴(95-digit number)
17768345876241935631…23152631625720869519
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
1.776 Γ— 10⁹⁴(95-digit number)
17768345876241935631…23152631625720869519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.776 Γ— 10⁹⁴(95-digit number)
17768345876241935631…23152631625720869521
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
3.553 Γ— 10⁹⁴(95-digit number)
35536691752483871262…46305263251441739039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.553 Γ— 10⁹⁴(95-digit number)
35536691752483871262…46305263251441739041
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
7.107 Γ— 10⁹⁴(95-digit number)
71073383504967742525…92610526502883478079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.107 Γ— 10⁹⁴(95-digit number)
71073383504967742525…92610526502883478081
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
1.421 Γ— 10⁹⁡(96-digit number)
14214676700993548505…85221053005766956159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.421 Γ— 10⁹⁡(96-digit number)
14214676700993548505…85221053005766956161
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
2.842 Γ— 10⁹⁡(96-digit number)
28429353401987097010…70442106011533912319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.842 Γ— 10⁹⁡(96-digit number)
28429353401987097010…70442106011533912321
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
5.685 Γ— 10⁹⁡(96-digit number)
56858706803974194020…40884212023067824639
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:57,893,623 XPMΒ·at block #6,831,184 Β· updates every 60s
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