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Block #2,293,476

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/12/2017, 1:50:42 PM Β· Difficulty 10.9542 Β· 4,537,711 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3ea2ec219bcfd22ca48d21d0e72cab26f8a93e860b12b72118fe74fe6a834353
View on Chainz β†—

Height

#2,293,476

Difficulty

10.954152

Transactions

2

Size

425 B

Version

2

Bits

0af44354

Nonce

345,408,286

Timestamp

9/12/2017, 1:50:42 PM

Confirmations

4,537,711

Mined by

⛏️ P2SHALTVRcequjpCCwHHurfN8PZ9iRn1KGjijP

Merkle Root

c14338b63c099f2b25cce2592f272f2f388f16afb91638e3700f23e12c3cdab1
Transactions (2)
Coinbase3a06ecb79d7ba0…047eb687abb303
1 in β†’ 1 out8.3300 XPM109 B
ALTVRceq…n1KGjijP
ac8458059ab8b2…985bb5ffd0d588
1 in β†’ 2 out20872.2751 XPM226 B
AGc4G3Md…FgVxh1VgATcbvWF6…7XYUkWNR
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.

1.580 Γ— 10⁹⁡(96-digit number)
15802613422572628142…04996784067241101439
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
1.580 Γ— 10⁹⁡(96-digit number)
15802613422572628142…04996784067241101439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.580 Γ— 10⁹⁡(96-digit number)
15802613422572628142…04996784067241101441
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
3.160 Γ— 10⁹⁡(96-digit number)
31605226845145256285…09993568134482202879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.160 Γ— 10⁹⁡(96-digit number)
31605226845145256285…09993568134482202881
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
6.321 Γ— 10⁹⁡(96-digit number)
63210453690290512570…19987136268964405759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.321 Γ— 10⁹⁡(96-digit number)
63210453690290512570…19987136268964405761
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
1.264 Γ— 10⁹⁢(97-digit number)
12642090738058102514…39974272537928811519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.264 Γ— 10⁹⁢(97-digit number)
12642090738058102514…39974272537928811521
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
2.528 Γ— 10⁹⁢(97-digit number)
25284181476116205028…79948545075857623039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.528 Γ— 10⁹⁢(97-digit number)
25284181476116205028…79948545075857623041
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:57,893,640 XPMΒ·at block #6,831,186 Β· updates every 60s
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