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Block #2,130,217

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/24/2017, 7:13:57 AM Β· Difficulty 10.9092 Β· 4,677,905 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9f433ae02a3487ffdd85e895e9b233860d7d2e99c8249ed5b0305a01ffe84451
View on Chainz β†—

Height

#2,130,217

Difficulty

10.909216

Transactions

3

Size

2.94 KB

Version

2

Bits

0ae8c25d

Nonce

354,191,457

Timestamp

5/24/2017, 7:13:57 AM

Confirmations

4,677,905

Mined by

⛏️ P2SHAUKcbFD8SeBZt5JSb5JRTMt6N3CsMfEZ1A

Merkle Root

03f426d0c3d3ca76b246d3cbeffeeab831d338ff3ee2ad38ea4c4521d3fa982c
Transactions (3)
Coinbasec16a3436489447…4df0b735b37dbc
1 in β†’ 1 out8.4300 XPM110 B
AUKcbFD8…CsMfEZ1A
ad62ba35a9cab0…0a68b52f21e520
1 in β†’ 2 out131518.4409 XPM225 B
AUEawiE3…GyTvR4e6AcXDnG1h…zL6LZ3ao
71bd6662e31f2a…23c702f621a5da
17 in β†’ 2 out1.5587 XPM2.53 KB
AU4PaUq3…No78btAoALs6jt4e…1goEPm8X
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.

1.096 Γ— 10⁹³(94-digit number)
10962755747273760510…39568435687270487039
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
1.096 Γ— 10⁹³(94-digit number)
10962755747273760510…39568435687270487039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.096 Γ— 10⁹³(94-digit number)
10962755747273760510…39568435687270487041
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
2.192 Γ— 10⁹³(94-digit number)
21925511494547521021…79136871374540974079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.192 Γ— 10⁹³(94-digit number)
21925511494547521021…79136871374540974081
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
4.385 Γ— 10⁹³(94-digit number)
43851022989095042043…58273742749081948159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.385 Γ— 10⁹³(94-digit number)
43851022989095042043…58273742749081948161
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
8.770 Γ— 10⁹³(94-digit number)
87702045978190084086…16547485498163896319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.770 Γ— 10⁹³(94-digit number)
87702045978190084086…16547485498163896321
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
1.754 Γ— 10⁹⁴(95-digit number)
17540409195638016817…33094970996327792639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.754 Γ— 10⁹⁴(95-digit number)
17540409195638016817…33094970996327792641
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:57,709,016 XPMΒ·at block #6,808,121 Β· updates every 60s
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