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Block #2,795,026

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/15/2018, 12:02:56 PM Β· Difficulty 11.6777 Β· 4,047,635 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
11f68b2c00c4b521c66f9292906ca77e82a5f864e9a6025fb1cc41a9e0a4acd8
View on Chainz β†—

Height

#2,795,026

Difficulty

11.677661

Transactions

2

Size

1.28 KB

Version

2

Bits

0bad7b33

Nonce

330,671,764

Timestamp

8/15/2018, 12:02:56 PM

Confirmations

4,047,635

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

521f0c1653b960ca822c5ef6378b2785f9ef36d614c7a237f1a54c857abfd85e
Transactions (2)
Coinbasef4b5ba4b381d97…a00555b9b92aaa
1 in β†’ 1 out7.3500 XPM110 B
AZtxQr2F…7grUWrUz
6e54dc7b0562ea…d4d798ee1b6af9
7 in β†’ 2 out15463.3775 XPM1.09 KB
ATdbDU6H…xTX3Wi8NAT7R24XJ…gwCnPYp5
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.

8.521 Γ— 10⁹⁡(96-digit number)
85212770991554713106…74649014485157463039
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
8.521 Γ— 10⁹⁡(96-digit number)
85212770991554713106…74649014485157463039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.521 Γ— 10⁹⁡(96-digit number)
85212770991554713106…74649014485157463041
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
1.704 Γ— 10⁹⁢(97-digit number)
17042554198310942621…49298028970314926079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.704 Γ— 10⁹⁢(97-digit number)
17042554198310942621…49298028970314926081
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
3.408 Γ— 10⁹⁢(97-digit number)
34085108396621885242…98596057940629852159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.408 Γ— 10⁹⁢(97-digit number)
34085108396621885242…98596057940629852161
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
6.817 Γ— 10⁹⁢(97-digit number)
68170216793243770484…97192115881259704319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.817 Γ— 10⁹⁢(97-digit number)
68170216793243770484…97192115881259704321
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
1.363 Γ— 10⁹⁷(98-digit number)
13634043358648754096…94384231762519408639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.363 Γ— 10⁹⁷(98-digit number)
13634043358648754096…94384231762519408641
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
2.726 Γ— 10⁹⁷(98-digit number)
27268086717297508193…88768463525038817279
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:57,985,723 XPMΒ·at block #6,842,660 Β· updates every 60s
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