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Block #2,758,331

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2018, 2:54:06 AM Β· Difficulty 11.6668 Β· 4,086,378 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e409caacae3b8b3c35785b953b0cc78222db1a3f5b3e8aa31208d31a1cd867ec
View on Chainz β†—

Height

#2,758,331

Difficulty

11.666769

Transactions

1

Size

200 B

Version

2

Bits

0baab15d

Nonce

416,102,854

Timestamp

7/21/2018, 2:54:06 AM

Confirmations

4,086,378

Mined by

⛏️ P2SHAQcCod1D35yFP193ZLrdU6VG9ykfUsdmN6

Merkle Root

aa94af87b9eb6a9736784ea513dbcd91af7d7424c88e19e8b2d912389195d37c
Transactions (1)
Coinbaseaa94af87b9eb6a…d912389195d37c
1 in β†’ 1 out7.3300 XPM110 B
AQcCod1D…kfUsdmN6
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.

2.980 Γ— 10⁹⁡(96-digit number)
29805902202841546999…89779839058442111999
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
2.980 Γ— 10⁹⁡(96-digit number)
29805902202841546999…89779839058442111999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.980 Γ— 10⁹⁡(96-digit number)
29805902202841546999…89779839058442112001
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
5.961 Γ— 10⁹⁡(96-digit number)
59611804405683093999…79559678116884223999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.961 Γ— 10⁹⁡(96-digit number)
59611804405683093999…79559678116884224001
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
1.192 Γ— 10⁹⁢(97-digit number)
11922360881136618799…59119356233768447999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.192 Γ— 10⁹⁢(97-digit number)
11922360881136618799…59119356233768448001
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
2.384 Γ— 10⁹⁢(97-digit number)
23844721762273237599…18238712467536895999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.384 Γ— 10⁹⁢(97-digit number)
23844721762273237599…18238712467536896001
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
4.768 Γ— 10⁹⁢(97-digit number)
47689443524546475199…36477424935073791999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.768 Γ— 10⁹⁢(97-digit number)
47689443524546475199…36477424935073792001
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
9.537 Γ— 10⁹⁢(97-digit number)
95378887049092950398…72954849870147583999
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:58,002,082 XPMΒ·at block #6,844,708 Β· updates every 60s
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