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Block #1,859,183

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/21/2016, 6:23:15 AM Β· Difficulty 10.6826 Β· 4,965,477 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fb17f650b5b523d7ce1556d9f32d7226bc347382d30246852917a6e5227dd172
View on Chainz β†—

Height

#1,859,183

Difficulty

10.682552

Transactions

2

Size

836 B

Version

2

Bits

0aaebbb8

Nonce

932,518,970

Timestamp

11/21/2016, 6:23:15 AM

Confirmations

4,965,477

Mined by

⛏️ P2SHAKLyoTT6HeAW62DeQuyYuRwipDyYmRhYFu

Merkle Root

84252917bf5f6b57b88e39ad05797dd5b30bd968a11aa4129d920af0013669c2
Transactions (2)
Coinbased6646502fcc58f…65c37b869f7432
1 in β†’ 1 out8.7600 XPM110 B
AKLyoTT6…yYmRhYFu
60414a1089b4fd…c4b9d71c1c4f26
4 in β†’ 1 out3999.9900 XPM636 B
AcDhjHA9…ebukETHz
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.

1.125 Γ— 10⁹⁴(95-digit number)
11250096195252677319…01101110034764062719
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
1.125 Γ— 10⁹⁴(95-digit number)
11250096195252677319…01101110034764062719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.125 Γ— 10⁹⁴(95-digit number)
11250096195252677319…01101110034764062721
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
2.250 Γ— 10⁹⁴(95-digit number)
22500192390505354639…02202220069528125439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.250 Γ— 10⁹⁴(95-digit number)
22500192390505354639…02202220069528125441
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
4.500 Γ— 10⁹⁴(95-digit number)
45000384781010709278…04404440139056250879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.500 Γ— 10⁹⁴(95-digit number)
45000384781010709278…04404440139056250881
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
9.000 Γ— 10⁹⁴(95-digit number)
90000769562021418556…08808880278112501759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.000 Γ— 10⁹⁴(95-digit number)
90000769562021418556…08808880278112501761
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
1.800 Γ— 10⁹⁡(96-digit number)
18000153912404283711…17617760556225003519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.800 Γ— 10⁹⁡(96-digit number)
18000153912404283711…17617760556225003521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,841,342 XPMΒ·at block #6,824,659 Β· updates every 60s
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