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Block #2,284,617

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/6/2017, 7:50:45 AM Β· Difficulty 10.9551 Β· 4,555,802 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
935eba70099cdf404bbcc5e3e722647e677d392a15e4b699589ae3bc31ce17f6
View on Chainz β†—

Height

#2,284,617

Difficulty

10.955148

Transactions

2

Size

426 B

Version

2

Bits

0af48490

Nonce

630,083,469

Timestamp

9/6/2017, 7:50:45 AM

Confirmations

4,555,802

Mined by

⛏️ P2SHAQruJjsHQkg2zf4Hxy2VLPxqpN8ZUqJ7Ds

Merkle Root

3b0db3550575f90d7b7e1d2581e85c5a0a0115b7e5be119a922c4e5bce6e8fc5
Transactions (2)
Coinbase29b14d2b2b63cc…5bef60090068d6
1 in β†’ 1 out8.3300 XPM110 B
AQruJjsH…8ZUqJ7Ds
93b8c1ec49b266…d30321f4c2f962
1 in β†’ 2 out1979.9900 XPM226 B
AYfMeY49…ct7j3CXuAS8Swa5k…emSJQqiE
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.

3.103 Γ— 10⁹⁴(95-digit number)
31039414212381717657…08245970428303316319
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
3.103 Γ— 10⁹⁴(95-digit number)
31039414212381717657…08245970428303316319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.103 Γ— 10⁹⁴(95-digit number)
31039414212381717657…08245970428303316321
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
6.207 Γ— 10⁹⁴(95-digit number)
62078828424763435314…16491940856606632639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.207 Γ— 10⁹⁴(95-digit number)
62078828424763435314…16491940856606632641
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
1.241 Γ— 10⁹⁡(96-digit number)
12415765684952687062…32983881713213265279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.241 Γ— 10⁹⁡(96-digit number)
12415765684952687062…32983881713213265281
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
2.483 Γ— 10⁹⁡(96-digit number)
24831531369905374125…65967763426426530559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.483 Γ— 10⁹⁡(96-digit number)
24831531369905374125…65967763426426530561
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
4.966 Γ— 10⁹⁡(96-digit number)
49663062739810748251…31935526852853061119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.966 Γ— 10⁹⁡(96-digit number)
49663062739810748251…31935526852853061121
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:57,967,677 XPMΒ·at block #6,840,418 Β· updates every 60s
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