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Block #2,076,058

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/18/2017, 12:26:35 PM Β· Difficulty 10.8445 Β· 4,740,474 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
01ccc98638c401463d98dcbe274638d755f3871b66b8e56f46652f9815fcba10
View on Chainz β†—

Height

#2,076,058

Difficulty

10.844484

Transactions

2

Size

723 B

Version

2

Bits

0ad83013

Nonce

1,825,082

Timestamp

4/18/2017, 12:26:35 PM

Confirmations

4,740,474

Mined by

⛏️ P2SHAXmJ1fASvMGXD76zpb8PvDusckmVKw8iSw

Merkle Root

21322a561e460c3e04a007b6f094ee0b6072553454429cfad1a69b0e17e19f09
Transactions (2)
Coinbase79742fac1c3d69…a8cc215422afd6
1 in β†’ 1 out8.5000 XPM109 B
AXmJ1fAS…mVKw8iSw
f4aba72ac4f384…0b4b76986ca63a
3 in β†’ 2 out2115.2799 XPM523 B
AXN3W3GL…ydH34przAKo2YYz6…sGvQnUrs
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.

1.681 Γ— 10⁹⁷(98-digit number)
16810396916766416810…08280423132908113919
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
1.681 Γ— 10⁹⁷(98-digit number)
16810396916766416810…08280423132908113919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.681 Γ— 10⁹⁷(98-digit number)
16810396916766416810…08280423132908113921
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
3.362 Γ— 10⁹⁷(98-digit number)
33620793833532833620…16560846265816227839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.362 Γ— 10⁹⁷(98-digit number)
33620793833532833620…16560846265816227841
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
6.724 Γ— 10⁹⁷(98-digit number)
67241587667065667241…33121692531632455679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.724 Γ— 10⁹⁷(98-digit number)
67241587667065667241…33121692531632455681
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
1.344 Γ— 10⁹⁸(99-digit number)
13448317533413133448…66243385063264911359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.344 Γ— 10⁹⁸(99-digit number)
13448317533413133448…66243385063264911361
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
2.689 Γ— 10⁹⁸(99-digit number)
26896635066826266896…32486770126529822719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.689 Γ— 10⁹⁸(99-digit number)
26896635066826266896…32486770126529822721
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:57,776,383 XPMΒ·at block #6,816,531 Β· updates every 60s
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