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Block #715,426

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2014, 7:46:52 PM Β· Difficulty 10.9541 Β· 6,092,372 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ec44485f59da68abe9f681dac8403650ea69df283a5613a7bf8ce029829dfa23
View on Chainz β†—

Height

#715,426

Difficulty

10.954132

Transactions

2

Size

1.11 KB

Version

2

Bits

0af441fc

Nonce

568,434,468

Timestamp

9/10/2014, 7:46:52 PM

Confirmations

6,092,372

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2af0b660a815501156b5fd14afe8477e7c7ba984a9be86a019a81348bb93bb8a
Transactions (2)
Coinbase2ed46129e7491f…bd4d26244dee2c
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
c197c6e48be9be…239194a195742c
6 in β†’ 1 out23.9900 XPM934 B
AX68fSXw…sD9P3rs3
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.

1.081 Γ— 10⁹⁷(98-digit number)
10815105827973864045…87459406801326825639
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
1.081 Γ— 10⁹⁷(98-digit number)
10815105827973864045…87459406801326825639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.081 Γ— 10⁹⁷(98-digit number)
10815105827973864045…87459406801326825641
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
2.163 Γ— 10⁹⁷(98-digit number)
21630211655947728090…74918813602653651279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.163 Γ— 10⁹⁷(98-digit number)
21630211655947728090…74918813602653651281
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
4.326 Γ— 10⁹⁷(98-digit number)
43260423311895456181…49837627205307302559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.326 Γ— 10⁹⁷(98-digit number)
43260423311895456181…49837627205307302561
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
8.652 Γ— 10⁹⁷(98-digit number)
86520846623790912362…99675254410614605119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.652 Γ— 10⁹⁷(98-digit number)
86520846623790912362…99675254410614605121
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
1.730 Γ— 10⁹⁸(99-digit number)
17304169324758182472…99350508821229210239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.730 Γ— 10⁹⁸(99-digit number)
17304169324758182472…99350508821229210241
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:57,706,417 XPMΒ·at block #6,807,797 Β· updates every 60s
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