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Block #2,862,405

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/1/2018, 8:30:24 AM Β· Difficulty 11.6744 Β· 3,982,871 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ba19007a1d4ae38137519148be7fbf2f30c31e118b1e9625f03446937e2e5a09
View on Chainz β†—

Height

#2,862,405

Difficulty

11.674383

Transactions

1

Size

200 B

Version

2

Bits

0baca459

Nonce

923,038,720

Timestamp

10/1/2018, 8:30:24 AM

Confirmations

3,982,871

Mined by

⛏️ P2SHAeSixGvg1BdoPzUuzeFzsEwyQCkuT1eefW

Merkle Root

f7392dc837176ad99f1a5903ca3df595eef0624a37c316fc3330c442e290abcd
Transactions (1)
Coinbasef7392dc837176a…30c442e290abcd
1 in β†’ 1 out7.3200 XPM110 B
AeSixGvg…kuT1eefW
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.

1.665 Γ— 10⁹⁴(95-digit number)
16653833215341629277…04511295761878892639
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
1.665 Γ— 10⁹⁴(95-digit number)
16653833215341629277…04511295761878892639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.665 Γ— 10⁹⁴(95-digit number)
16653833215341629277…04511295761878892641
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
3.330 Γ— 10⁹⁴(95-digit number)
33307666430683258554…09022591523757785279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.330 Γ— 10⁹⁴(95-digit number)
33307666430683258554…09022591523757785281
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
6.661 Γ— 10⁹⁴(95-digit number)
66615332861366517108…18045183047515570559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.661 Γ— 10⁹⁴(95-digit number)
66615332861366517108…18045183047515570561
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
1.332 Γ— 10⁹⁡(96-digit number)
13323066572273303421…36090366095031141119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.332 Γ— 10⁹⁡(96-digit number)
13323066572273303421…36090366095031141121
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
2.664 Γ— 10⁹⁡(96-digit number)
26646133144546606843…72180732190062282239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.664 Γ— 10⁹⁡(96-digit number)
26646133144546606843…72180732190062282241
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
5.329 Γ— 10⁹⁡(96-digit number)
53292266289093213687…44361464380124564479
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:58,006,643 XPMΒ·at block #6,845,275 Β· updates every 60s
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