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Block #2,663,888

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/16/2018, 4:14:44 PM Β· Difficulty 11.6499 Β· 4,169,025 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a9050e3dca1dc78cd2a5805aa784bfd6bc2c61ea27151ad231f13cf7ebc000fe
View on Chainz β†—

Height

#2,663,888

Difficulty

11.649860

Transactions

2

Size

723 B

Version

2

Bits

0ba65d3a

Nonce

257,166,312

Timestamp

5/16/2018, 4:14:44 PM

Confirmations

4,169,025

Mined by

⛏️ P2SHAV55TNyNzCwe1VoN5fJC44AEVPAK783uo4

Merkle Root

310189879da9951776027accda7692337d7ba65a3083a7db4781ae9fd19e066e
Transactions (2)
Coinbase44dd80cc6e448a…f9948cd92b336b
1 in β†’ 1 out7.3700 XPM110 B
AV55TNyN…AK783uo4
4a2be2751ba769…03932cd493c33c
3 in β†’ 2 out9092.0102 XPM522 B
AFyiVMM5…axfNM8abATjQu5dH…QgLvsbWp
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.

3.392 Γ— 10⁹⁷(98-digit number)
33922850957985637989…72007863251012157439
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
3.392 Γ— 10⁹⁷(98-digit number)
33922850957985637989…72007863251012157439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.392 Γ— 10⁹⁷(98-digit number)
33922850957985637989…72007863251012157441
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
6.784 Γ— 10⁹⁷(98-digit number)
67845701915971275978…44015726502024314879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.784 Γ— 10⁹⁷(98-digit number)
67845701915971275978…44015726502024314881
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
1.356 Γ— 10⁹⁸(99-digit number)
13569140383194255195…88031453004048629759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.356 Γ— 10⁹⁸(99-digit number)
13569140383194255195…88031453004048629761
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
2.713 Γ— 10⁹⁸(99-digit number)
27138280766388510391…76062906008097259519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.713 Γ— 10⁹⁸(99-digit number)
27138280766388510391…76062906008097259521
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
5.427 Γ— 10⁹⁸(99-digit number)
54276561532777020783…52125812016194519039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.427 Γ— 10⁹⁸(99-digit number)
54276561532777020783…52125812016194519041
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
1.085 Γ— 10⁹⁹(100-digit number)
10855312306555404156…04251624032389038079
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:57,907,477 XPMΒ·at block #6,832,912 Β· updates every 60s
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