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Block #2,096,775

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2017, 5:51:20 AM Β· Difficulty 10.8719 Β· 4,746,081 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
20b80ccdbe46ff4114cb8c0a8c8fa199348e3da5c37133d2c963d9a60f83601e
View on Chainz β†—

Height

#2,096,775

Difficulty

10.871918

Transactions

2

Size

882 B

Version

2

Bits

0adf3600

Nonce

112,207,469

Timestamp

5/2/2017, 5:51:20 AM

Confirmations

4,746,081

Mined by

⛏️ P2SHAc4rssydX37KyBg9FfRmVGixVJimKTjU2U

Merkle Root

b32dc32608f57516ea280f35db7874318e559baf822a6f71f457d6b8855789b1
Transactions (2)
Coinbasef4a71fcf930139…3b7cc8d5a493e8
1 in β†’ 1 out8.4600 XPM110 B
Ac4rssyd…imKTjU2U
9eee5d55f94695…cd692ed5b71348
5 in β†’ 2 out38.1350 XPM683 B
AJ5Y738R…4a68DogJAN4s4bb4…8sL1AkRU
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.

2.720 Γ— 10⁹²(93-digit number)
27204034912108879244…98813385195531838759
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
2.720 Γ— 10⁹²(93-digit number)
27204034912108879244…98813385195531838759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.720 Γ— 10⁹²(93-digit number)
27204034912108879244…98813385195531838761
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
5.440 Γ— 10⁹²(93-digit number)
54408069824217758488…97626770391063677519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.440 Γ— 10⁹²(93-digit number)
54408069824217758488…97626770391063677521
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
1.088 Γ— 10⁹³(94-digit number)
10881613964843551697…95253540782127355039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.088 Γ— 10⁹³(94-digit number)
10881613964843551697…95253540782127355041
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
2.176 Γ— 10⁹³(94-digit number)
21763227929687103395…90507081564254710079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.176 Γ— 10⁹³(94-digit number)
21763227929687103395…90507081564254710081
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
4.352 Γ— 10⁹³(94-digit number)
43526455859374206791…81014163128509420159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.352 Γ— 10⁹³(94-digit number)
43526455859374206791…81014163128509420161
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:57,987,195 XPMΒ·at block #6,842,855 Β· updates every 60s
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